From A Emma cycles 4 miles NE to B, then 6 miles NW to C. Find angle BAC

This is a 3-4-5 right angle and angle abc is the 90.

Have you drawn a diagram?
Sitkadiver is correct, if you travel NE then NW the angle you make is 90 degrees (a right angle)
The question has given you the magnitude of the opposite and adjacent sides. You just need to pick the right relationship from SOHCAHTOA to find the angle.