Consider the given triangle.

Looking at the labels on the given figure, we can see that

m ∠ G F H = m ∠ H G F .

We can write this by using a congruence statement.

∠ G F H ≅ ∠ H G F

Now, let's recall the classification of triangles.

Classification of Triangles
Scalene Triangle	A scalene triangle is a triangle in which all three sides have different lengths.
Isosceles Triangle	An isosceles triangle is a triangle that has two congruent sides and two base angles with the same measure.
Equilateral Triangle	An equilateral triangle is a triangle in which all the sides are congruent.
Acute Triangle	An acute triangle is a triangle where all angles are less than $9 0^{\circ}$ or $\frac{π}{2} .$
Obtuse Triangle	An obtuse triangle is a triangle with exactly one an angle whose measure is greater than $9 0^{\circ}$ or $\frac{π}{2} .$
Right Triangle	A right triangle is a specific type of triangle that contains one angle of $9 0^{\circ} .$

Since the given triangle have two congruent angles, triangle $F G H$ is an isosceles triangle. We want to find $\overline{F H} .$ To do so, we will use the Converse of the Isosceles Triangle Theorem.

Converse of the Isosceles Triangle Theorem
If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

Using this theorem, let's show the congruent sides.

As a result, $\overline{G H} ≅ \overline{F H} .$ Therefore, $F H = 12 .$

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