In order to find what ordered pair is a solution to the equation, one way to do it would be to plug the points into the equation for x and y.
To start, first plug in choice A, (18,-4):
-4=-59(18)-6
When you simplify, you would result in -4=-1068 which is not a true statement. This means that the choice (18, -4) cannot be the answer.
Next, plug (27,9) into the equation:
9=-59(27)-6
When simplified, you should result in 9=-1599 which is also not a true mathematical statement, meaning (27,9) is also not the answer.
Now, plug in (18,4):
4=-59(18)-6
This results in 4=-1068 which is not the answer either.
Finally, plug in (27, -21):
-21=-59(27)-6
Because it simplifies to -21=-1599, meaning the point is also not a solution, it appears to be that none of your points given are valid solutions to the equation y=-59x-6.