As per the language given it is mod 2 and mod 3.
So, we know in this case the number of states will be 2 * 3 = 6 (total remainder pair is 6)
We design a machine for
And we know machine of
Now machine for,
Here identified remainder of a’s and identified remainder of b’s.
In the above machine, there are four grades,
So, the final state must the common state (Intersection) of states and .
Because language is,
here AND means intersection.