The shaded region in the Venn diagram is "natural numbers"
Recall that the natural numbers are positive integers and start from 1.
[tex]\N=1,2,3,4,5,6,7\ldots[/tex]We are asked to identify which of the given options contains a value of n that does not belong to the natural numbers.
Let us simplify each of the given equations.
Option A:
[tex]\begin{gathered} -3n=-9 \\ 3n=9 \\ n=\frac{9}{3} \\ n=3 \end{gathered}[/tex]3 is a valid natural number so it does belong to the shaded region.
Option B:
[tex]\begin{gathered} 2n=8 \\ n=\frac{8}{2} \\ n=4 \end{gathered}[/tex]4 is a valid natural number so it does belong to the shaded region.
Option C:
[tex]\begin{gathered} -2n=4 \\ n=\frac{4}{-2} \\ n=-2 \end{gathered}[/tex]-2 is not a natural number, therefore, it does not belong to the shaded region.
Option D:
[tex]\begin{gathered} -3n=-6 \\ 3n=6 \\ n=\frac{6}{3} \\ n=2 \end{gathered}[/tex]2 is a valid natural number so it does belong to the shaded region.
Therefore, the equation in option C contains a value of n that should NOT be placed in the shaded region of the Venn diagram.