She made 6 patches of cookies because if she uses 1/8 per batch and 3/4 x2 equals 6/8 , she made 6 batches.
The next number is 38. The pattern is 7, 16, 8, 27, 9; if you look at the first 4 numbers, you notice that it counts to 7, 8, 9. Then you have 16 and 27, if the pattern continues; the next number is 38.