I take this to be interpreted as:

What is the probability that the sum of the numbers on the dice
is divisible by 3, given that it is a two digit number?

If that is the correct interpretation, then since we are given
that the sum is a two-digit number, the sum can only be 10, 11, 
or 12, the ones colored red below: 

⚀⚀   ⚀⚁   ⚀⚂   ⚀⚃   ⚀⚄  ⚀⚅

⚁⚀   ⚁⚁   ⚁⚂   ⚁⚃   ⚁⚄  ⚁⚅

⚂⚀   ⚂⚁   ⚂⚂   ⚂⚃   ⚂⚄  ⚂⚅

⚃⚀   ⚃⚁   ⚃⚂   ⚃⚃   ⚃⚄  ⚃⚅

⚄⚀   ⚄⚁   ⚄⚂   ⚄⚃   ⚄⚄  ⚄⚅

⚅⚀   ⚅⚁   ⚅⚂   ⚅⚃   ⚅⚄  ⚅⚅

Since we are given that the sum is a two-digit number, we can take
away all the rolls whose sum is not a 2-digit, but only a a 1-digit
number, and we will just have the red ones left as our reduced
sample space:


                          ⚃⚅

                     ⚄⚄  ⚄⚅

                ⚅⚃   ⚅⚄  ⚅⚅ 

And the only one of those rolls whose sum is divisible by 3 is
the one whose sum is 12, ⚅⚅.

That's 1 out of 6.

Answer 1/6.

Edwin