A and B are acute angles with tan A = 1/2 and tan B = 1/3…

Step 1. The tangent of the sum. $\tan(A + B) = \dfrac{\frac{1}{2} + \frac{1}{3}}{1 - \frac{1}{2} \cdot \frac{1}{3}} = \dfrac{\frac{5}{6}}{\frac{5}{6}} = 1$.

Step 2. The range of $A + B$. Both angles are acute, so $0 < A + B < \pi$.

Step 3. The angle. The only angle in $(0, \pi)$ with tangent $1$ is $\dfrac{\pi}{4}$.