The correct order for constructing the bisector of angle $\angle XYZ$ is:

1. Step B: With the tip of a pair of compasses at $Y$, draw an arc which crosses $XY$ and $YZ$.
2. Step A: Place the tip of the compasses where your arc crosses $XY$. Draw an arc in the middle of the angle.
3. Step D: Without changing the width of the compasses, place the tip where your first arc crosses $YZ$. Draw an arc which crosses your previous arc.
4. Step C: Draw a line from the point where the arcs meet to $Y$.

This sequence ensures the angle bisector is drawn accurately.

Would you like an explanation of why these steps work or more details about compass constructions?

Here are some related questions:

1. What is the purpose of using a compass in geometric constructions?
2. Can the angle bisector method be applied to obtuse angles?
3. How do you ensure precision when constructing arcs?
4. What are other uses of a compass in constructions besides bisectors?
5. What is the mathematical significance of an angle bisector in triangle properties?

Tip: Always keep your compass setting unchanged when transferring arcs to maintain consistency.