In mathematics, the word "sphere" refers to the hollow $x^2+y^z+z^2=r^2$ and the word "ball" refers to the solid $x^2+y^2+z^2<r^2$. This question asks about a conducting spherical shell. Such an object is therefore hollow. "The electric field is zero inside of a solid conductor" applies only to a solid conductor. It doesn't apply to hollow conductors.
For a hollow conducting shell, the electric field of charges outside the conductor are negated in the cavity inside of the conducting shell. Such a conducting shell is called a Faraday cage. You can deduce for yourself that "The electric field is zero inside of a conductor" is just a generalization of how Faraday cages work.
Your hollow conducting shell is a Faraday cage. The charge $Q$ spreads to the outside of the Faraday cage. Thus, the points inside of the Faraday cage are shielded from $Q$. All that matters is $q$. Apply Coulomb's law to $q$ and you get the answer.
Another way of thinking about it is that points inside the sphere see charge $q$ and points outside the sphere see both charges $q$ and $Q$.
The Shell Theorem
The shell theorem totally applies here. Charge $Q$ is equally distributed in a sphere. Therefore, according to the shell theorem charge $Q$ exerts no electric field on the inside of the sphere. All that is left is point charge $q$.