Answer
$-z$
Work Step by Step
We know that $q $ is negative and we want $\vec{v}\times\vec{B}$ to have the opposite direction to $\vec{F}$. Since $\vec{v}\times\vec{B}$ points to $+y$,
the negative scalar q will cause $q( \vec{v}\times\vec{B} )$ to point to $-\mathrm{y}$, like $\vec{F}$ does.
Now, we use the right hand rule (see fig. 3.19 on p. 53) :
Outstretch your right arm and turn your hand so your thumb points up.
The fingers are pointing to the right (the fingers represent $\vec{v}$ in the $+x$ direction, and the thumb $\vec{v}\times\vec{B}$ in the $+y$ direction).
Swipe your fingers roughly for a right angle. The fingers now point to the front of you. This is the $-z$ direction, when compared to the diagram.
This is where $\vec{B}$ points.
