evaḿ bahu-vidhā yajñā
vitatā brahmaṇo mukhe
karma-jān viddhi tān sarvān
evaḿ jñātvā vimokṣyase

Translation of Bhagavad Gita 4.32

All these different types of sacrifice are approved by the Vedas, and all of them are born of different types of work. Knowing them as such, you will become liberated.

Commentary by Sri A.C. Bhaktivedanta Swami Prabhupada of Gaudiya Sampradaya:

Different types of sacrifice, as discussed above, are mentioned in the Vedas to suit the different types of worker. Because men are so deeply absorbed in the bodily concept, these sacrifices are so arranged that one can work either with the body, with the mind, or with the intelligence. But all of them are recommended for ultimately bringing about liberation from the body. This is confirmed by the Lord herewith from His own mouth.

Commentary by Sri Vishvanatha Chakravarthi Thakur of Gaudiya Sampradaya:

Brahmanah means the Vedas. The phrase vitata brahmano mukhe whose literal meaning is “spread in the mouth of the Vedas” actually means “clearly spoken of by the Vedas themselves.” Karma jan means based on the actions of the body, mind and words.

Commentary by Sri Ramanuja of Sri Sampradaya:

4.32 Thus there are many kinds of Kamra Yoga, which are spread out for the attainment of the Brahman. That means, they lead to the realisaion of the true nature of the individual self. Know that all these are forms of Karma Yoga, which have been previoulsy defined and diversified, as born of actions. That means, know them as resulting from occasional and obligatory rites performed day by day. Knowing thus, observing them in the manner prescribed, you will be released. It has been stated that actions have the form of knowledge because of the inclusion of knowledge in them. Now Sri Krsna explains the predominance of the component of knowledge in such actions which include knowledge within themselves.

Commentary by Sri Sridhara Swami of Rudra Sampradaya:

Now Lord Krishna concludes His appraisal of yagnas or offerings of worship to propitiate the Supreme Lord in karma yoga or prescribed Vedic activities in order to adequately praise yagnas performed in jnana yoga or the cultivation of Vedic knowledge. Thus yagna is directly prescribed by the Vedic scriptures which are authorised by the Supreme Lord. Yet it should be understood that all yagnas are accomplished by activity whether it is of the mind, of speech or of the body. This activity material and not of the reality of the atma or soul which is purely spiritual. By comprehending this and devoting oneself to acquiring spiritual knowledge one will attain moksa or liberation from transmigratory existence.

Commentary by Sri Madhvacharya of Brahma Sampradaya:

The word brahmano is referring directly to the Supreme Lord Krishna the recepient of all yagnas or offerings of worship, through His attribute the Brahman or the spiritual substratum pervading all existence. Such yagnas according to the qualifiyation of the performer may be mentally performed, orally performed or physically performed. Knowing this and performing ordained activities according to the injunctions of the Vedic scriptures one will attain moksa or liberation from the cycle of birth and death in the material existence. Performing yagna according to one’s rank and station in life is what is being given here and whether it is mental, oral or physical the activity is still performed by concerted effort. So what is ordained by the injunctions of the Vedic scriptures should never be ignored or disregarded.

Now begins the summation.

The words vitata brahmano mukhe means everything should be offered to the Supreme Lord. In the Brahman Vaivartaka Purana it states that: In all yagnas the Supreme Lord alone is to be propitiated. This means that every activity and all endeavours one undertakes should be in harmony with the injunctions and ordinances of the Vedic scriptures which are in complete and total harmony with the divine will of the Supreme Lord. No other alternative is tenable or acceptable for a human being.

Commentary by Sri Keshava Kashmiri of Kumara Sampradaya:

Lord Krishna confirms the authenticity of the previous described yagnas or offerings of worship as being sanctioned by the Vedic scriptures by the word evam meaning of this kind and the different types have been explained in detail in the parampara or disciplic succession and have been transmitted from spiritual master to disciple in the tradition of the Vedic culture. All of the before mentioned yagnas are performed by mind, by speech or by the physical body but their actions are of a transitory nature and the atma or soul is eternal. So these actions and the atma are not invariably connected. Thus comprehending this in reality one will be free from samsara the cycle of birth and death caused by actions.

Commentary by Sri Adi Shankaracharya of Advaita Sampradaya:

4.32 Evam, thus; bahu-vidha yajnah, various kinds of sacrifices as described; vitatah, lie spread; mukhe, at the mouth, at the door; brahmanah, of the Vedas. Those which are known through the Vedas- as for instance, ‘We offer the vital force into speech’, etc.-are said to be vitatah, spread, elaborated; mukhe, at the mouth; brahmanah, of the Vedas. Viddhi, know; tan, them; sarvan, all; to be karmajan, born of action, accoplished through the activities of body, speech and mind, but not born of the Self. For the Self is actionless. Hence, jnatva, knowing; evam, thus; vimoksyase, you will become liberated from evil. By knowing thus- ‘These are not my actions; I am actionless and detached’-You will be freed from worldly bondage as a result of this full enlightenment. This is the purport. Through the verse beginning with, ‘The ladle is Brahman’ etc., complete Illumination has been represented as a sacrifice. And sacrifices of various kinds have been taught. With the help of [Some translate this as: As compared with…-Tr.] those (sacrifices) that are meant for accomplishing desireable human ends, Knowledge (considered as a sacrifice) is being extolled: How?

Commentary by Sri Abhinavagupta of Kaula Tantra Sampradaya:

4.32 Evam etc. All these sacrifices have been detailed in the mouth of i.e., at the entrance to, i.e., as means to [attain], the Brahman. In them there lies the practice of actions as common factor. By knowing in this manner, you too shall attain liberation from bondage. The speciality here is this :
and decide for themselves, those explanations and the etymological interpretations offered by our revered preceptors. So, look ! What is the use of the sport of criticising the statements of those commentators ? Hence let us stick to only what we have begun with.

Sanskrit Shloka Without Transliteration Marks:

evam bahu-vidha yajña
vitata brahmano mukhe
karma-jan viddhi tan sarvan
evam jñatva vimoksyase

Sanskrit to English Word for Word Meanings:

evam — thus; bahu-vidhāḥ — various kinds of; yajñāḥ — sacrifices; vitatāḥ — are spread; brahmaṇaḥ — of the Vedas; mukhe — through the mouth; karma-jān — born of work; viddhi — you should know; tān — them; sarvān — all; evam — thus; jñātvā — knowing; vimokṣyase — you will be liberated.