Rolling three dice...am I doing this correctly?

As a check: here is a different approach. There are three choices for the odd die out: left, middle, or right. For each choice of odd die out, there are $6$ choices for its value and then $5$ values for the value of the pair. That makes $3\cdot6\cdot5=90$ outcomes for two of three the same. There are a total of $6^3=216$ total possibilities, giving a probability of $\frac{90}{216}=\frac{5}{12}$.

Yes your answer is correct. $${3\choose 2}\cdot\frac{1}{6}\cdot\frac{5}{6} = \frac{5}{12}$$

Good job!