For most students this problem will be outside their ordinary
mathematical experience.
There is no frequentlyused technique which may be just applied in
this new situation.
Talk helps enormously in a problem like this. Questions to prompt
thinking include :
 What difference can you think of between the front and the rear
wheels ?
 What is the connection between the front and rear wheels which,
for example, wouldn't be possessed by two unicyclists going along
the path ?
These suggestions from the hint page may be useful :

Find a bicycle and experiment.

Trace a curve on paper and imagine a cyclist following that
curve with the front wheel, and then consider the possibilities for
the back wheel ?
Above all this is a good
problem not to rush .
Leave the way into this problem left
open and allow students to bring along fresh thoughts
from time to time. The emerging solution will be much more
satisfying and the process a much better experience of real new
mathematics emerging.