If the point is translated 8 units to the left the x-coordinate of the original point is decreased by 8. If the point is translated down 9 units the y-coordinate of the original point is decreased by 9.
So if the original point is (4,6) then the new point is ((4-8), (6-9))=(-4, -3)
The distance between these two points can be found with the Pythagorean Theorem. Because the distance between the two points is equal to the length of the hypotenuse of a right triangle with sides equal to the displacements we made for the transformation.
d^2=8^2+9^2
d^2=64+81
d^2=145
d=√145 units
d≈12.04 units (to the nearest hundredth of a unit)
So the closest measurement that you have to choose from is 12 units.