Final answer:
The lumbricals and palmar interossei muscles of the hand are most likely paralyzed, which are responsible for flexing the metacarpophalangeal joints and adducting the fingers.
Step-by-step explanation:
The muscles most likely paralyzed in a patient unable to flex the metacarpophalangeal joints of the ring and index finger and unable to adduct these fingers are the lumbricals and the palmar interossei muscles. The lumbricals are responsible for flexing the metacarpophalangeal joints and extending the interphalangeal joints of the fingers. On the other hand, the palmar interossei muscles adduct and flex the fingers at the metacarpophalangeal joints while also extending each finger at the interphalangeal joints. This combination of flexion of metacarpophalangeal joints and finger adduction suggests the involvement of these intrinsic muscles of the hand.