Hi Manpreet,
My understanding is that generally speaking you could use pour s'amuser à la campagne (to enjoy ourselves/ have fun in the countryside) for a roughly similar meaning to pour profiter de la campagne (to enjoy the countryside).
I haven't done that writing exercise. Perhaps it specifies the second phrase and so might not accept the use of s'amuser à instead.
I believe that s'amuser de would mean to laugh at rather than to enjoy.
I hope this helps :)
