Solution

Given expression:

$ABC+A\overline{B}CD+E\overline{F}+AD$

Number of inputs in product terms:

$ABC=3$

$A\overline{B}CD=4$

$E\overline{F}=2$

$AD=2$

Total inputs for AND gates:

$3+4+2+2=11$

There are $4$ product terms, so OR gate needs $4$ inputs.

Total gate inputs:

$11+4=15$