Question

How to solve the problem

Answer 1

The rule is: segments on one side of the angle bisector are proportional to the corresponding segments on the other side.

(4x -5)/6 = (2x)/8
You can solve as is, or you can clear fractions first. Here is the "as is" solution.
.. x(2/3 -1/4) = 5/6 . . . . . . . add 5/6 -x/4
.. x = (5/6)/(5/12) = 2 . . . . . divide by the coefficient of x

Selection A is appropriate.