The method shown in my diagram works this way ...
1) threaten to use check to force the king up a rank if he reaches the opposition square
2) threaten to flank the king (when he goes to the edge you move up) when he reaches a position near the edge of the board if he does not move to the opposition square
3) when he is near the edge use the box method to put the king in a box created by the rook.
From the starting position there are 2 quicker ways to move the enemy king from the third rank. I think the term "box method" is probably used to describe any move that does not occur in the first method.