The ans is A - unique circuit (only a not gate required )
the question is saying With a single 8:1 mux how to convert a 16:1 mux ....... we can manage the extra variable D (say four variables are A B C D ) by putting D according to the function in the input line of 4:1 mux and there are 2 possibility either D or D' . for this we need a extra not gate .
if the Question would be like this "by using 8 * 1 MUX if 4 variable function is realised than the circuit is ?"
then the answer will be like :
8:1 MUX means it can support (with only one 8:1 MUX) 3 variables ,the input line will be 8 , select lines are 3 (variables) and one output line. and now 16:1 MUX it can support (with only one 16:1 MUX) 4 variables ,the input line will be 16 , select lines are 4 (variables) and one output line.
So the question can be converted like this .... how many 8:1 MUX is needed to build a 16:1 MUX !!!
and i assume you know how to calculate it ..... upper ceiling ( (16/8) + (16/8^2) ) = 3
3 8:1 MUX is required .