Solve for y in the given diagram.

The diagram shows two parallel lines intersected by two transversals, forming a triangle. The arrows on the horizontal lines indicate they are parallel. The tick marks on the two slanted sides of the triangle indicate that these sides are equal in length, making it an isosceles triangle.

When a transversal intersects two parallel lines, the alternate interior angles are equal.
The angle $2y$ is an alternate interior angle to the bottom-left angle of the triangle. Therefore, the bottom-left angle of the triangle is $2y$.
The angle $56^\circ$ is an alternate interior angle to the bottom-right angle of the triangle. Therefore, the bottom-right angle of the triangle is $56^\circ$.

In an isosceles triangle, the angles opposite the equal sides are equal. Since the two slanted sides of the triangle are marked as equal, the base angles (the angles opposite these sides) must be equal.
So, the bottom-left angle of the triangle is equal to the bottom-right angle of the triangle.

From Step 2 and Step 3, we have:

Divide both sides by 2:

The value of $y$ is $28^\circ$.