A wire runs left to right and carries a current in the direction shown. What is the direction of the magnetic field at point Z?

is this positive charge current, or electron current? It matters. Us your hand rules in your text.

To determine the direction of the magnetic field at point Z, we can use the right-hand rule for current-carrying wire.

1. Extend the right hand with the thumb pointing in the direction of the current flow (from left to right in this case).
2. Curl the fingers of the right hand around the wire. The direction in which fingers curl represents the direction of the magnetic field.

In this scenario, since the current is flowing from left to right, if you curl your fingers around the wire, your fingertips will point inwards towards the opposite side of the wire. Therefore, the direction of the magnetic field at point Z will be into the plane of the paper.

Can't help you on this one