Some of you are making too much of this.  The question is 
asking you how many possible functions of two (also three, four) 
inputs are there.

It is not asking you to count only functions that have 
commonly known names, like AND, OR, NAND, NOR.

You can determine this by looking at the truth table.  
Let's take the case of 2 inputs, A and B.

A  B  |  function
------|------------
0  0  |    w
0  1  |    x
1  0  |    y
1  1  |    z


You know that there are four different input combinations, 
as shown by the number of rows in the truth table.  And, 
you know that for each input combination, the truth table 
specifies an output.  We are showing them (in general) as
 w,x,y,z in the truth table above where each of these letters 
must correspond to a 0 or a 1.

For AND: w,x,y =0 and z=1.
For OR: w=0 and x,y,z=1.

Another case is w,z=0 and x,y=1.  That function also has 
a common name, which is in the book.

Another case is w,y,z=0 and x=1.  As far as I know, that 
function does not have a common name.  Still, it is a function.

So, since each unique specification of w,x,y, and z corresponds 
to a different function, and w,x,y, and z can be specified 
individually as 0 or as 1, how many possible functions are there?

OK?

Yale Patt