FORK
FORK is the four-letter answer. Start at the F in row 4, column 6, move down to the O in row 5, column 6, continue down to the R in row 6, column 6, and turn left to the K in row 6, column 5. It is a compact edge route with one turn and two straight segments.
If you are comparing your board carefully, the sequence is 1 at row 4, column 6; 2 at row 5, column 6; 3 at row 6, column 6; 4 at row 6, column 5. The path spans three rows and two columns, visits four edge cells, and ends after assigning the first four cells.