A wire is carrying current vertically downwards. To the east of the wire, the magnetic field would be directed to

A wire is carrying current vertically downwards. To the east of the wire, the magnetic field would be directed out of the plane of the paper

The current in the wire is in the downward direction. Using the right-hand thumb rule we see that the direction of the magnetic field to the east of the wire is coming out of the plane of the paper.