jmc

Since the line is parallel to $y=4x+6$, we know that its slope is 4. Thus the equation of the line is $y=4x+b$ where $b$ is the $y$-intercept. Plugging $(5,10)$ into this gives $10=4\cdot 5+b\Rightarrow b=\boxed{-10}$ which is what we wanted.