Entry 1: the four-letter path
Trace HERB through these cells: 1 at row 4, column 2; 2 at row 4, column 3; 3 at row 5, column 3; 4 at row 6, column 3. Reading those letters in path order gives H → E → R → B.
Make one move right, then continue down twice. The route has one turn and two straight segments, spanning three rows and two columns. It visits one edge cell and no corner cells. Both row 4, column 2 and row 6, column 3 have three open orthogonal neighbors on the raw board. Confirming this entry assigns four cells and leaves 22 open cells for the other paths.