To find the missing value to make the point \((4, __)\) on the equation \(y = -6x^2 + 2\), we need to substitute \(x = 4\) into the equation and solve for \(y\).
Starting from the equation:
\[ y = -6x^2 + 2 \]
Substituting \(x = 4\):
\[ y = -6(4^2) + 2 \]
Calculating \(4^2\):
\[ 4^2 = 16 \]
Now plug this back into the equation:
\[ y = -6(16) + 2 \] \[ y = -96 + 2 \] \[ y = -94 \]
Thus, the missing value is:
\[ y = -94 \]
So the point would be \((4, -94)\).