jmc

Let $x$ represent the number of gallons the tank holds when it is full. We know that the difference between $\frac{7}{8}$ full and $\frac{1}{2}$ full is 12 gallons, so we set up an equation and solve for $x$. $$\begin{array}{rl}12& =\frac{7}{8}x-\frac{1}{2}x\Rightarrow \\ 12& =\frac{3}{8}x\Rightarrow \\ 12\cdot \frac{8}{3}& =x\Rightarrow \\ 32& =x\end{array}$$ The tank holds $\boxed{32}$ gallons when it is full.