Answer
14 electrons.
Work Step by Step
The values of $m_{\mathcal{l}}$ range from $-\mathcal{l}$ to $\mathcal{l}$, or $2\mathcal{l}+1$ values.
For each of those values, there are 2 possible values of $m_{s}$, which are $-\frac{1}{2},\frac{1}{2}$.
Therefore, we see that the total number of states for a particular $\mathcal{l}$ is $2(2\mathcal{l}+1)$.
For $\mathcal{l}=3$, there are 2(2(3)+1) = 14 electrons in the subshell.
