In plain words
Thus many kinds of yajña are spread at the mouth of the Veda. Know them all to arise from action; understanding this, you will be liberated.
Word for word
Thus yajñas of many kinds are spread out at the mouth of the Veda; know them all as born of action; knowing thus, you will be freed.
The commentators
Bhagavadgītābhāṣyam· bhāṣya
एवं यथोक्ता बहुविधा बहुप्रकारा यज्ञाः वितताः विस्तीर्णाः ब्रह्मणो वेदस्य मुखे द्वारे वेदद्वारेण अवगम्यमानाः ब्रह्मणो मुखे वितता उच्यन्ते ; तद्यथा ‘वाचि हि प्राणं जुहुमः’(ऐ. आ. ३ । २ । ६) इत्यादयः । कर्मजान् कायिकवाचिकमानसकर्मोद्भावान् विद्धि तान् सर्वान् अनात्मजान् , निर्व्यापारो हि आत्मा । अत एवं ज्ञात्वा विमोक्ष्यसे अशुभात् । न मद्व्यापारा इमे, निर्व्यापारोऽहम् उदासीन इत्येवं ज्ञात्वा अस्मात् सम्यग्दर्शनात् मोक्ष्यसे संसारबन्धनात् इत्यर्थः ॥ ३२ ॥
In plain words
So all the sacrifices described so far, of every kind and sort, are said to be 'spread out in the mouth' — that is, at the gateway — of Brahman, of the Veda: understood, that is, through the Veda's own gateway, in Brahman's mouth, as in texts like 'we offer prāṇa into speech itself' (Ai. Ār. 3.2.6) and others like it. Know all of these — everything born of action, arising from what you do with body, speech, and mind — to be not born of the Self at all, since the Self has no activity whatsoever. Knowing this, you will be freed from evil. 'These are not my doings; I have no activity, I remain untouched' — knowing this, through this very right vision, you will be freed from the bondage of the cycle of birth and death. That is the meaning.
Close to the Sanskrit
Thus, sacrifices as described, of many kinds, of many sorts, are called 'spread out' — expansive — 'in the mouth', that is, the door, of Brahman, of the Veda — that is, understood through the door of the Veda, in the mouth of Brahman; for example, 'into speech, indeed, we offer prāṇa' (Ai. Ār. 3.2.6) and other such texts. Know all these, born of action, arising from bodily, vocal, and mental action, to be not born of the Self — for the Self is without any activity. Therefore, knowing this, you will be released from evil. 'These are not my doings; I am without activity, indifferent' — knowing this, from this right vision, you will be freed from the bondage of transmigration. This is the meaning.