I notice that the point $(4,7)$ is on the graph of $y=3f\left(2x\right)+1$, which means that $7=3f\left(2\cdot 4\right)+1$. Simplifying, I get that $6=3f\left(8\right)$, or $f\left(8\right)=2$. This means that the point $(8,2)$ is on the graph of $y=f(x)$. To find the sum of coordinates of that point, I just add $8$ and $2$, and get $10$. 
Given that the point $(4,7)$ is on the graph of $y=3f\left(2x\right)+1$, there is one point that must be on the graph of $y=f(x)$. What is the sum of coordinates of that point?