Probability of the sum of two dice being less than six, knowing that said sum is a multiple of 4

Two dice are thrown, What is the probability that the sum of the two faces of the dice is less than 6, if we know that said sum is a multiple of 4?

These kinds of exercises are not my forte, but I'm pretty sure my answer is correct. The solution given is $\frac{3}{10}$, but I think the real solution is $\frac39$, I realized this is conditional probability, so I did $$\frac{\frac{3}{36}}{\frac{9}{36}}$$ Which gave me my answer. Are there any errors? Thanks.

I agree with you. There are $3$ ways to get $4$, $5$ ways to get $8$ and $1$ way to get $12$