Answer :

To solve the problem, we need to find the value of the function [tex]\( g(N) = 3N^2 - 2N - 6 \)[/tex] at [tex]\( N = -2 \)[/tex].

Let's substitute [tex]\( N = -2 \)[/tex] into the function:

[tex]\[ g(-2) = 3(-2)^2 - 2(-2) - 6 \][/tex]

First, we need to calculate each term separately:

1. Calculate [tex]\( (-2)^2 \)[/tex]:
[tex]\[ (-2)^2 = 4 \][/tex]

2. Multiply this result by 3:
[tex]\[ 3 \times 4 = 12 \][/tex]

3. Calculate [tex]\( -2 \times (-2) \)[/tex]:
[tex]\[ -2 \times (-2) = 4 \][/tex]

4. Now, sum these results and subtract 6:
[tex]\[ g(-2) = 12 + 4 - 6 \][/tex]

5. Finally, perform the addition and subtraction:
[tex]\[ 12 + 4 = 16 \][/tex]
[tex]\[ 16 - 6 = 10 \][/tex]

Thus, the value of [tex]\( g(-2) \)[/tex] is 10. Therefore, the correct answer is:

C) 10