The number of subshells associated with $n=4andm=-2$ quantum numbers is 

Principal quantum number (n) signifies the shell or orbit number. Form the number of values of

azimuthal quantum number (I), we can calculate number of subshell present in a shell as, $I=\mathrm{0....}\left(n-1\right)$ So, When $n=4$ The permissible value of $I$ and subshell are

$I=0\to$s-subshell

$=1\to$p-subshell        

$=2\to d-$subshell

$=3\to f-$subshell

But, here value of I are restricted by the value of magnetic quantum number, $m=-2,$Where, m depends  on I as $m=-\mathrm{1....0....}+I$

So, $m=-2$ value is possible for two subshells, viz, $l=3\left(f-subshell\right)$ and $l$=2 (d-subshell) only.

$l=3\Rightarrow m=-3,-2-1,0+1,+2,+3$

$I=2\Rightarrow m=-2,-1,0,+1,+2$