3.1 Calculate, with reasons, the value of x. 2.3.2 Calculate, with reasons, the value of y.

$$\text{AC} \parallel \text{GF}$$

Reason: Given (indicated by arrows on the lines).

$$\angle DEF = \angle BAC$$

Reason: Corresponding angles, since AC $\parallel$ GF and AD is a transversal.

$$x = 54^\circ$$

Reason: Substitution.

The value of $x$ is $\boxed{\text{54}^\circ}$.

2.3.2 Calculate, with reasons, the value of $y$.

$$\angle ACB + \angle BAC + \angle ABC = 180^\circ$$

Reason: Sum of angles in a triangle.

$$\angle ACB = 180^\circ - 54^\circ - 63^\circ = 63^\circ$$

Reason: Calculation.

$$\text{AC} \parallel \text{GF}$$

Reason: Given (indicated by arrows on the lines).

$$\angle BGE = \angle ACB$$

Reason: Alternate interior angles, since AC $\parallel$ GF and CG is a transversal.

$$y = 63^\circ$$

Reason: Substitution.

The value of $y$ is $\boxed{\text{63}^\circ}$.