The number of subshells associated with n = 4 and m = -2 quantum numbers is:

🧠 The Quantum Address Filter We need to identify which subshells ($l$) in shell $n=4$ are capable of containing an orbital with the orientation $m=-2$.

🗺️ The Value Audit

1. Principal ($n=4$): Allowed $l$ are 0(s), 1(p), 2(d), 3(f).
2. Magnetic ($m=-2$): For a magnetic number to exist, the condition is $l \geq |m|$.
3. Filtering:
   • $l=0, 1$: $|m|$ limit is too low ($m$ cannot reach 2).
   • $l=2 (d)$: $m \in \{-2, -1, 0, 1, 2\}$. (Match!)
   • $l=3 (f)$: $m \in \{-3, -2, -1, 0, 1, 2, 3\}$. (Match!) The subshells are 4d and 4f.

⚡ The "|m| Boundary" Shortcut A subshell houses an orbital $m$ if $l$ is at least $|m|$. Since $|-2|=2$, only $l=2$ and $l=3$ subshells in the 4th shell contain it. Total = 2.

⚠️ Common Traps Mistaking "subshells" for "orbitals." While there are 2 subshells, there are many more orbitals in total. The question specifically asks for the sub-level count.

$\boxed{\text{Answer: 2}}$