4-Input NAND Gate Reduction
Do not read this answer if this is homework :-).

You get "action" only when all presented inputs are 1
 1111 = 0.  All other xxxx = 1
A 3 input gate will deal with 111 and give 0
But the next gate has to deal with 10
 It "knows" how to deal with 11
 So, invert the 0 from the 3 input gate and NAND it with the final 1
QED

(A 2 input NAND (or 3 or 4 or ... input) knows how to be an inverter with only a little help from you. )