Answer:
ABDECFA
Explanation:
We start at A.
Remaining: BCDEF
The nearest unvisited neighbor to A is B, with a distance of 1.
Remaining: CDEF
The nearest unvisited neighbor to B is D, with a distance of 37.
Remaining: CEF
The nearest unvisited neighbor to D is E, with a distance of 27.
Remaining: CF
The nearest unvisited neighbor to E is C, with a distance of 3.
Remaining: F
The nearest (and only) unvisited neighbor to C is F, with a distance of 10.
We then loop back around to A, which is 11 away from F.