I claim the ornamental design for a towel hanger rack, as shown and described.
FIG. 1 is a front view of a towel hanger rack showing our new design;
FIG. 2 is a right side view thereof;
FIG. 3 is a left side view thereof;
FIG. 4 is a top view thereof;
FIG. 5 is a bottom view thereof; and,
FIG. 6 is a rear view thereof.
The broken line of the pedestal sink and the towel is included for the purpose of illustrating environment structure and forms not part of the claimed design.