Figure A and figure B are both regular polygons. The sum of the perimeter of figure

Choice A is correct. It’s given that figure A and figure B (not shown) are both regular polygons and the sum of the perimeters of the two figures is $63 \text{inches}$. It’s also given that $x$ is the number of sides of figure A and $y$ is the number of sides of figure B, and that the equation $3x+6y=63$ represents this situation. Thus, $3x$ and $6y$ represent the perimeters, in inches, of figure A and figure B, respectively. Since $6y$ represents the perimeter, in inches, of figure B and $y$ is the number of sides of figure B, it follows that each side of figure B has a length of $6 \text{inches}$.

Choice B is incorrect. The number of sides of figure B is $y$, not $6$.

Choice C is incorrect. Since the perimeter, in inches, of figure A is represented by $3x$, each side of figure A has a length of $3 \text{inches}$, not $6 \text{inches}$.

Choice D is incorrect. The number of sides of figure A is $x$, not $6$.