Factor-augmenting technologies (Acemoglu and Restrepo 2018c)
Chain rule! To make it simple call $\tilde{L} = A_L L$ and $\tilde{K} = A_K K$, so that

$$
Y = F(\tilde{K}, \tilde{L})
$$

so that

$$
\frac{\partial Y}{\partial L} = \frac{\partial \tilde{L}}{\partial L}\frac{\partial F}{\partial \tilde{L}} = A_L F_L(A_K K, A_L L)
$$

the trick here is that you should read $F_L$ as the derivative of $F$ with respect to its second argument.