for n=4 total 2^4=16 bit strings are possible, each bit string represents a vertex.
Now each vertex is connected to 4 other vertices. Why???
for example, vertex 0000 is connected to every other vertex where bit differs in exactly one-bit position so 0000 is connected to 0001, 0010, 0100, 1000
Similarly, each vertex is connected to 4 other vertices so the total number of edges in H4 = (16*4)/2 = 32
Now total number of edges in complete graph = C(16,2) = 120
Number of edges in H4(complement) = 120-32 = 88