Given that the point $(4,7)$ is on the graph of $y=f(x)$, there is one point that must be on the graph of $2y=3f(4x)+5$. What is the sum of the coordinates of that point?
So, to find the point that must be on the graph of $2y=3f(4x)+5$, I need to plug in $x=1$, since that would make $4x=4$. Then, I can use the equation $2y=3f(4x)+5$ to find the corresponding value of $y$. If $x=1$, then $2y=3f(4)+5=3(7)+5=26$. So, $y=13$. Therefore, the point that must be on the graph of $2y=3f(4x)+5$ is $(1,13)$. The sum of the coordinates of that point is $1+13=14$.

