For what values of `a ` and ` b` the intercepts cut off n the coordinate axes by the line `a x+b y+8=0` are equal in length but opposite in signs to those cut off by the line `2x-3y+6=0` on the axes.

Explanation

To solve the problem, we need to find the values of \( a \) and \( b \) such that the intercepts cut off on the coordinate axes by the line \( ax + by + 8 = 0 \) are equal in length but opposite in sign to those cut off by the line \( 2x - 3y + 6 = 0 \).

### Step-by-Step Solution:

1. **Find the intercepts of the line \( 2x - 3y + 6 = 0 \)**:
- **X-intercept**: Set \( y = 0 \).
\[
2x + 6 = 0 \implies 2x = -6 \implies x = -3
...