The only way to answer this is to brute force it.

Step 1: Write down all the multiples of 13 between 10 and 100

13, 26, 39, 52, 65, 78, 91

Step 2: Find which one has digits that sum to 11

1+3 = 4, 2+6 = 8, 3+9 = 12, 5+2 = 7, 6+5 = 11, 7+8 = 15, 9+1 = 10

The answer is 65

Step 1: Write down all the multiples of 13 between 10 and 100

13, 26, 39, 52, 65, 78, 91

Step 2: Find which one has digits that sum to 11

1+3 = 4, 2+6 = 8, 3+9 = 12, 5+2 = 7, 6+5 = 11, 7+8 = 15, 9+1 = 10

The answer is 65