Because he divided his cake into 6 equal pieces, we can represent the eaten and remaining amounts with fractions.
Remember that a fraction is the ratio of number of pieces over the total pieces.
So, we need to figure out how much cake needs to be subtracted.
We know his sister ate 1/6 of the cake and he ate 3/6 of the cake. We can add these fractions together because they have common denominators.
3/6+1/6=4/6
So, we need to subtract 4/6 from the whole:
6/6-4/6=2/6, so 2 slices out of the 6 remain.