Word-by-word meaning:
śreyaḥ anyat – śreyas is one (path); uta – and preyaḥ eva anyat – preyas is quite another. te ubhe – Those two; nānārthe – with different destinations; sinītaḥ puruṣam – bind a person. bhavati sādhu – There is felicity; ādadānasya – for one who chooses; śreyaḥ – śreyas; 
tayoḥ – between the two. yaḥ vṛṇīte – One who chooses; preyaḥ – preyas; u hīyate – is indeed deprived; arthāt – of the (supreme) goal. 

Translation:
śreyas is one (path) and preyas is quite another. Those two, with different destinations, bind a person. There is felicity for one who chooses śreyas between the two. One who chooses preyas is indeed deprived of the (supreme) goal.

Explanation:

• Glorification of the student: Swamiji explains that Lord Yama is glorifying the vedānta student in general by presenting the two fundamentally distinct paths that present themselves to a jīva in life. Only humans have the free will to choose between these two paths, and because of this choice, they also face conflict.
• The path of preyas (material pursuit): The veda-pūrva portion deals with various physical, verbal, and mental actions (karma). These actions are performed to gain sense pleasures by improving sense objects, sense organs, and one’s environment to attain worldly pleasures (anātma-sukham). Swamiji points out that this path of action (karmamārga or pravṛtti mārga) is called preyas because it appeals to the common man’s instinct. It is naturally liked and attractive. In this path, happiness depends entirely on external factors and on “what I have,” which turns the jīva into an extrovert.
• The path of śreyas (spiritual pursuit): In contrast, vedānta deals with knowledge (jñāna) and its benefit, which is the joy of the self (ātma-sukham). This path of knowledge (jñānamārga or nivṛtti mārga) is called śreyas. Here, the focus completely shifts from “what I have” to “what I am.” It deals with the transformation of the self, naturally drawing the mind inward. While preyas is attractive, Swamiji notes that śreyas is ultimately “desirable” because it is eternally good for everyone.
• The divergence of the two paths: Swamiji emphasizes that a jīva cannot follow both paths as primary goals simultaneously because they are diagonally opposite. Moving toward one naturally means moving away from the other. The two paths have totally distinct results and lead to entirely different destinations.
• The consequences of choice: The verse asserts that the one who chooses preyas will ultimately be deprived of the supreme goal (brahman). On the other hand, the intelligent, discriminative person who chooses śreyas attains true felicity. While steadfastly following śreyas, one’s secondary material goals might still be fulfilled, but the primary focus remains liberation.
• Clarification on bhakti: Swamiji clarifies that bhakti yoga is not a separate, third path. If devotion is expressed in the form of rituals, japa, or meditation on a form, it falls under karmamārga (preyas). However, if devotion is expressed in the form of enquiring into the true nature of bhagavan, it becomes jñānamārga (śreyas).