To prove that DE || AC and CB || Mx, we can use properties of parallel lines and angles.

### a) Prove that DE || AC:

1. **Parallel Lines and Corresponding Angles:**
- Observe that ∠EBC is a right angle, meaning it measures 90°.
- Given that ∠ACM is marked as 48°, therefore ∠DCB = 90° - 48° = 42°.

2. **Use of Alternate Interior Angles:**
- Since ∠EBC and ∠ACM are corresponding angles in terms of the transversal CB, and both angles are equal, DE is parallel to AC by the definition of corresponding angles with a transversal.

### b) Prove that CB || Mx:

1. **Using Angle Properties:**
- Given: ∠DCB = ∠ACM = 48°.
- Since both of these angles are equal and located on alternate sides of the transversal CM, CB must be parallel to Mx.

Therefore, the pairs of lines DE and AC, CB and Mx are parallel based on the corresponding and alternate angle criteria.