Let's determine which of the given coordinates satisfies the equation [tex]\(4x - 2y = -12\)[/tex].
We will test each option to see which one satisfies this equation by plugging in the [tex]\(x\)[/tex] and [tex]\(y\)[/tex] values provided.
### Option [A]: [tex]\((-20, 2)\)[/tex]
Substitute [tex]\(x = -20\)[/tex] and [tex]\(y = 2\)[/tex] into the equation:
[tex]\[ 4(-20) - 2(2) = -80 - 4 = -84 \][/tex]
Clearly, [tex]\(-84 \neq -12\)[/tex]. So, [tex]\((-20, 2)\)[/tex] does not satisfy the equation.
### Option [B]: No solution
This would be the case if none of the provided points satisfy the equation after checking all the options.
### Option [C]: [tex]\((0, 6)\)[/tex]
Substitute [tex]\(x = 0\)[/tex] and [tex]\(y = 6\)[/tex] into the equation:
[tex]\[ 4(0) - 2(6) = 0 - 12 = -12 \][/tex]
This satisfies the equation because [tex]\(-12 = -12\)[/tex].
### Option [D]: [tex]\((-2, 2)\)[/tex]
Substitute [tex]\(x = -2\)[/tex] and [tex]\(y = 2\)[/tex] into the equation:
[tex]\[ 4(-2) - 2(2) = -8 - 4 = -12 \][/tex]
This also satisfies the equation because [tex]\(-12 = -12\)[/tex].
Conclusion:
Since option [C] [tex]\((0, 6)\)[/tex] satisfies the original equation [tex]\(4x - 2y = -12\)[/tex], the correct answer is:
[tex]\[ \boxed{(0, 6)} \][/tex]
