Anne,
They might appear similiar, but the holding directions you just provided mean that one airplane would be holding fifteen miles east of ABC VORTAC, and one airplane will be holding fiteen miles west of ABC VORTAC.
This is because the 15 DME fix on the 086 radial is fifteen miles east.
The 15 DME fix on the 266 radial is fifteen miles west.
Graphically, they'll both be depicted similiarly; both will have the hold depicted on the west side of the fix (to the left, if you're drawing it with north at the top of your paper). However, if the holding directions are to hold west on the 15 DME fix, 086 radial ABC VORTAC...the hold will take place fifteen miles east of ABC VORTAC. The inbound leg to the fix will be away from the VORTAC, tracking the 086 radial outbound to the 15 DME fix.
If the holding directions are to hold west of the 15 DME fix, 266 radial ABC VORTAC, the hold will take place fifteen miles west of ABC VORTAC. The inbound leg to the fix will be toward the VORTAC, tracking the 266 radial inbound to the 15 DME fix. If the book depicts other than that, or your instructor indicates otherwise, both the book, and your instructor, are wrong.