YouSigma

ಏಷಾ ತೇSಭಿಹಿತಾ ಸಾಂಖ್ಯೇ ಬುದ್ಧಿರ್ಯೋಗೇ ತ್ವಿಮಾಂ ಶೃಣು ।
ಬುದ್ಧ್ಯಾ ಯುಕ್ತೋ ಯಯಾ ಪಾರ್ಥ ಕರ್ಮ ಬಂಧಂ ಪ್ರಹಾಸ್ಯಸಿ ॥೩೯॥
eṣā teSbhihitā sāṃkhye buddhiryoge tvimāṃ śṛṇu |
buddhyā yukto yayā pārtha karma baṃdhaṃ prahāsyasi ||39||
Gist of the sloka:
I have taught you the science of atma. I am now going to instruct you and how to master it. O Partha, once you assimilate it, you would be free of karma bindings.
Explanation:
Lord Krishna says, so far, I was instructing you in the science of Shaankya. I will now instruct you on how to achieve it.
This is also known as Vedic Shaankya [that which upholds Vedic concepts] and that which was given by Sri Kapila Vasudeva [an avatar of Lord] to his mother Devahuti. Shaankya means that which gives our correct path and knowledge. It is due to these reasons ancients called the science which gives our right path as Shaankya.
Yoga is that which gives a path/solution/method/process which leads towards Lord. If we remove the Lord in such yoga, then its not considered yoga but a meaningless process. It is not the same yoga as mentioned by Patanjali in his yoga sutras. Of the various types of yoga, some are related to medical, physical flexibility, breathe science [pranayama] etc., practice of which does not require the concept of Lord.
It is not that practice of these yoga does not have benefits. Those benefits include obtaining specific siddis [powers] including magic/illusion etc., Those siddis does not lead us to mukthi but is utilized to amaze the populace and obtain fame. Vedas caution us not to be behind obtaining siddis and even demonstrate them. For such actions lead us away from Lord.
It is like the story of the person who spent 10-15 years in intense yoga to get the power/siddi to walk on water. It does not lead him to mukthi or enhance his knowledge of self. Rather the same aspect of crossing the water could have been achieved by paying a small token to the boat keeper. Those years could have enhanced his knowledge which would be with him irrespective of his many births.
Neither does one get mukthi immediately after obtaining the sacred knowledge. One should clear-up/experience the previous karma [prarabdha, that which has started to act] before reaching the elevated state.
The yoga being taught here by Lord Krishna is about science of Atma; selfawareness and how to reach the Lord. Gita is about how to achieve the final mukthi and understanding of soul and its relationship with the Lord.
Lord now talks about the science of the soul [self-realization], by treading which path a person can overcome the attachment of karmas and achieve mukthi. Lord now talks about the methods and means of achieving the same.
There are various books which instruct us of how to live from outside perspective. There is very little books which talk about the way we need to fashion our lives from inside leading to mukthi. How long should one meditate, in fact what should we meditate upon? What thoughts should we let our memory consist of?
Just with external rituals, dress, ceremonies etc., we achieve nothing. We need inner knowledge, wisdom and mental/memory state, that which leads to mukthi. The knowledge and our thoughts should be so aligned, that our inner and external actions are the same and there is one set of thoughts aligned to actions, leading to pleasing of the Lord.
Our belief and integrity should be same. Inner achievement in this direction is more important than external actions. We need knowledge but more importantly we need the right knowledge of self-realization leading to God realization. The knowledge should set us free from the cycle of the birth and death leading to final emancipation. Lord describes these in the next verses.