Discrete Math with Mod

Question

If $b \equiv 3 \pmod{12}$, what is $8b \pmod{12}$?

We can write $b=12q+3$. Then with some algebra $8b=12(8q+2)$.

This is causing me problems because there is not number plus $12(8q+2)$ to tell us the remainder. Is it just zero?

Answer 1

we have $$b\equiv 3 \mod 12$$ then $$8b\equiv 24\equiv 0\mod 12$$