OUT: left, then up
The three-letter entry is OUT. Begin with O at row 2, column 3, move left to U at row 2, column 2, and finish by moving up to T at row 1, column 2. Read those letters in that order as you trace. The change from a leftward step to an upward step happens at U, giving the route one turn and two straight segments.
Check the U at that turn. There are two Us on this board, but this entry uses row 2, column 2. Its final T is at row 1, column 2; T appears three times overall, so do not stop at the spelling alone. The route spans two rows and two columns, with no diagonal move.
Only the final cell touches the edge; this route visits no corner. The starting O has three open orthogonal neighbors, while the ending T has one. Those counts describe the board around the endpoints. After checking all three letters and both moves, you have accounted for 3 cells, leaving 18 for the other answers.