The answer is $\boxed{\text{C. }42, 48}$.
The sequence is $2, 8, 14, 20, 26, 32, 38, \dots$. Each number in the sequence is $6$ more than the previous number. Therefore, the next two numbers in the sequence are $42$ and $48$.
Option A is incorrect because $46$ is not $6$ more than $2$.
Option B is incorrect because $50$ is not $6$ more than $44$.
Option C is correct because $48$ is $6$ more than $42$.
Option D is incorrect because $42$ is not $6$ more than $40$.
Option E is incorrect because $26$ is not $6$ more than $32$.