Answer
$B=\color{blue}{30.9^\circ}$
Work Step by Step
Using the Sine Law,
$\dfrac{\sin A}{a} = \dfrac{\sin B}{b} \\
\dfrac{\sin 45.6^\circ}{789} = \dfrac{\sin B}{567}\\
\sin B = \dfrac{567 \sin 45.6^\circ}{789} \\
\sin B \approx 0.5134 \\
\color{blue}{B \approx 30.9^\circ}\quad \text{or}\quad \color{red}{B\approx 180^\circ-30.9^\circ \;=\; 149.1^\circ}
$
If $B=30.9^\circ$, then, since $A+B+C=180^\circ$,
$C = 180^\circ-A-B \\
C = 180^\circ-45.6^\circ-30.9^\circ \\
C = 103.5^\circ$.
Thus, such a triangle exists.
If $B=149.1^\circ$, then, since $A+B+C=180^\circ$,
$C = 180^\circ-A-B \\
C = 180^\circ-45.6^\circ-149.1^\circ \\
C = -14.7^\circ$.
Thus, there is no such triangle.
All told, there is exactly one solution: $\color{blue}{B=30.9^\circ}.$
