To determine the value of [tex]\( q^2 - p^2 \)[/tex] given [tex]\( q = 4 \)[/tex] and [tex]\( p = 2 \)[/tex], follow these steps:
1. Start by calculating [tex]\( q^2 \)[/tex]:
[tex]\[
q = 4 \implies q^2 = 4^2 = 16
\][/tex]
2. Next, calculate [tex]\( p^2 \)[/tex]:
[tex]\[
p = 2 \implies p^2 = 2^2 = 4
\][/tex]
3. Subtract [tex]\( p^2 \)[/tex] from [tex]\( q^2 \)[/tex]:
[tex]\[
q^2 - p^2 = 16 - 4 = 12
\][/tex]
Therefore, the value of [tex]\( q^2 - p^2 \)[/tex] is [tex]\( 12 \)[/tex].
Thus, the correct choice is:
D. 12
