Question

find the value of y

Explanation:

Step1: Use the Angle - Bisector Theorem

Since \(LH\) is the angle - bisector of the angle formed at \(H\), we have \(8y=6y + 12\).

Step2: Solve the equation for \(y\)

Subtract \(6y\) from both sides of the equation \(8y-6y=6y + 12-6y\).
This gives \(2y=12\).
Divide both sides by \(2\): \(y=\frac{12}{2}\).

Answer:

\(y = 6\)