Concept:
The Glass Transition Temperature ($T_g$) is highly sensitive to the presence of plasticizers. Plasticizers are small molecules that fit between polymer chains, increasing the space between them and making them more mobile.
Step 1: Analyzing Assertion (A).
Nylon 6 is a polyamide that contains amide groups capable of forming hydrogen bonds with water molecules. When water is absorbed, it acts as a plasticizer, reducing the intermolecular forces between the nylon chains. This makes the chains more mobile at lower temperatures, effectively decreasing the $T_g$. Thus, (A) is correct.
Step 2: Analyzing Reason (R).
Absorption of moisture causes swelling of the Nylon 6 fiber, not dissolution. Partial dissolution would imply the polymer chains are breaking away and entering a liquid state, which does not happen when nylon simply gets damp or wet. Thus, (R) is incorrect.