From the K-map:

Grouping:

A̅B̅C̅D̅ + A̅B̅CD̅ + ABC̅D̅ + ABC̅D + ABCD + ABCD̅ + AB̅C̅D̅ + AB̅CD̅
Simplify each pair:

A̅B̅D̅ + ABC̅ + ABC + AB̅D̅
Final simplification:

B̅D̅ + AB