In the pair 20 : 6 the second number counts how many factors the first number has, counting 1 and the number itself. Complete the analogy: 48 : ?

20 has the factors 1, 2, 4, 5, 10 and 20 — six of them, which matches the pair given. The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48, so the count is 10. The trap 9 comes from leaving 48 itself out of the list; 8 comes from counting only the even factors, 2, 4, 6, 8, 12, 16, 24 and 48; and 6 comes from stopping the list at 8, at 1, 2, 3, 4, 6, 8, instead of carrying it to the end.