There should only be 2 numbers with a length of 6 as described in the question.

I tried 2^6 and got 64
Then I tried 2^5*3 and got 96

There are no more combinations of 6 prime numbers that would give me a two digit number.

From the answer choices, you can figure out that there are not many such numbers possible. So listing down all the possible numbers would be a good strategy.

First find out what is the minimum number which has 6 prime factors. That will be 2X2X2X2X2X2 = 64

Now you can get the next greater number which will have 6 prime factors by increasing one factor from 2 to 3 (next possible prime number). So the next number is 2X2X2X2X2X3 = 96

If you further increase any factor (2 to 3 or 3 to 4), the result will cross 100, so 2 is the answer.

2*2*2*2*2*2 = 64

and 2*2*2*2*2*3 = 96

If you try susbstituting 3 for 2 any further we will move on to 3 digit numbers.

Hence answer is only 2 such double digit numbers exist