To solve the system of equations using the substitution method, we first substitute the expression for \( x \) from the first equation into the second equation.
We have the following equations:
- \( x = y - 4 \)
- \( x + 8y = 2 \)
Now, we can substitute \( x \) in the second equation:
\[ (y - 4) + 8y = 2 \]
Now, we can simplify and solve for \( y \):
\[ y - 4 + 8y = 2 \] \[ 9y - 4 = 2 \] \[ 9y = 2 + 4 \] \[ 9y = 6 \] \[ y = \frac{6}{9} = \frac{2}{3} \]
Now that we have the value of \( y \), we can substitute it back into the first equation to find \( x \):
\[ x = y - 4 = \frac{2}{3} - 4 \] \[ x = \frac{2}{3} - \frac{12}{3} = \frac{2 - 12}{3} = \frac{-10}{3} \]
Thus, the solution to the system of equations is:
\[ \left( \frac{-10}{3}, \frac{2}{3} \right) \]
So, the point is:
\[ \left( -\frac{10}{3}, \frac{2}{3} \right) \]
However, none of the provided responses exactly match with \(\left( -\frac{10}{3}, \frac{2}{3} \right)\). It seems like the right option is not included in your list.
Nonetheless, as per the calculations performed:
The solution to the system is: \[ \boxed{\left( -\frac{10}{3}, \frac{2}{3} \right)} \]