In plain words
By worshipping through one’s own work Him from whom beings arise and by whom all this is pervaded, a person attains perfection.
Word for word
Having worshipped by one's own duty Him from whom is the coming forth of beings, by whom all this is pervaded, a human being finds perfection.
The commentators
Bhagavadgītābhāṣyam· bhāṣya
यतः यस्मात् प्रवृत्तिः उत्पत्तिः चेष्टा वा यस्मात् अन्तर्यामिणः ईश्वरात् भूतानां प्राणिनां स्यात् , येन ईश्वरेण सर्वम् इदं ततं जगत् व्याप्तं स्वकर्मणा पूर्वोक्तेन प्रतिवर्णं तम् ईश्वरम् अभ्यर्च्य पूजयित्वा आराध्य केवलं ज्ञाननिष्ठायोग्यतालक्षणां सिद्धिं विन्दति मानवः मनुष्यः ॥ ४६ ॥
In plain words
'Yataḥ' means: from whom. From whom the stirring of beings — their coming into being, or their activity — arises; and 'beings' here means living creatures. He is the Lord who rules from within them. And by him all this world is stretched out — pervaded, filled through. Worship that Lord with your own work, the work already set out here for each varṇa: honour him with it, serve him with it. Doing that, a human being gains just this much — the success whose mark is fitness to stand firm in knowledge.
Close to the Sanskrit
'Yataḥ' — from which, that is, from whom; from whom the arising — the origination, or the activity — of beings, that is, of living creatures, comes to be, from that Lord who is the inner ruler; and by whom, by that Lord, all this world is stretched out, that is, pervaded — having worshipped, that is, having honoured, having propitiated, that Lord by one's own work, the work stated before for each varṇa, a man, a human being, obtains only that success whose mark is fitness for steadfastness in knowledge.