Mate, you can download my flashcards and take a look at slides 81-84. All the approaches to find GCF and LCM are there. Hope it helps.
Solving the question:
Always find the prime factors, as fluke showed. Then, remember that GCF is formed by the shared prime factors.
The 36's prime factors box has: 2, 2, 3, 3
(1) 12's prime box has 2, 2, 3. A 3 is missing, so not sufficient
(2) 9's prime box has 3, 3. Not sufficient as well (two 2's missing)
If you combine them, you will have two shared 2's and two shared 3's, which are the same as the prime factors of 36. So, both are sufficient. A number that is divisible by 9 and by 12 will also be divisible by 36.