Video solution:

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Written solution:

Let $ab$ be the two-digit number in question. Then, it follows that the number obtained by reversing its digits is $ba.$ Therefore, in order for $ab$ to satisfy the property in the question: $$\begin{align*}10(a + b) + a + b &=132\\11(a + b)&=132\\a+b&=12.\end{align*}$$ The only possible solutions $(a,b)$ to this equation, where $a,b$ are both one digit, are: $$(3,9), (4,8), (5,7), (6,6),$$$$(7,5), (8,4),(9,3).$$ As such, there are $7$ solutions.

Thus, B is the correct answer.