To add 2 negative binary numbers, change them into 2's complement form, and then add it.
So in this case,
- $-(14)_{10}$ = $00001110_2$
- $-(15)_{10}$ =$00001111_2$
2's complement of $(00001110)_2 \longrightarrow 11110001+1 = 11110010$
2's complement of $(00001111)_2 \longrightarrow 11110000+1 = 11110001$
add them to get the solution:
$(11110010)_2$ + $(11110001)_2= (11100011)_2$
Option $(A)$ is correct.