Start w/ the smallest number of "lenght" 6, i.e. 2^6 = 64
Next, replace one of the 2s with 3 to get 2^5*3=32*3 =96

Any other prime added in the above fashion will be a 3 digit number, so the answer is two (64 and 96)

Muzali, can you please explain a little further. I did not fully understand your explanation.

What he meant is that you have to multiply 6 (this is the length) primes and get two-digit positive integers. To do that you have to multiply with the lowest possible primes. So 2x2x2x2x2x2=2^6=64 is the lowest number you can get and it's a two digit number so it fits what we are looking for. The next lowest possible number would be 2x2x2x2x2x3=2^5*3 which is 96, also fits. The next one is 2x2x2x2x3x3, which is a 3 digit number, so this doesn't fit. It's obvious that no other 6 length primes will fit coz they will just get bigger and bigger in numbers. The only possible two-digit numbers are 64 and 96, and more to the point there are only two possible two-digit integers with the stated length of 6.

Hope it's clearer now.