Plan B (NENESEENWNWWNNEEE) allows Robby to reach his gift without hitting any trees.
How to determine direction?
A. NENNEENWWNNESE:
This plan results in Robby hitting two trees: one after going south twice and one after going east twice.
B. NENESEENWNWWNNEEE:
This plan allows Robby to reach the gift without hitting any trees. He moves north twice, east once, north once, east twice, south once, west twice, north twice, and finally east once to reach the gift.
C. NENSEENNWWNENEE:
This plan results in Robby hitting one tree after going north twice.
D. NENSEENWNWWNNEEE:
This is the same plan as option C and results in Robby hitting one tree after going north twice.
Therefore, the only plan that allows Robby to get his gift without hitting any trees is B. NENESEENWNWWNNEEE.