If you would like to know who paints the largest part of the fence, you can calculate this using the following steps:
three sections of the fence ... 3 sections
four equal sized boards ... 4 boards
3 * 4 = 12 boards
Alex: 1/6 of 12 boards = 1/6 * 12 = 2 boards
Bobby: twice as much as Alex = 2 * 2 boards = 4 boards
Charles: 1 board
David: 12 - 2 - 4 - 1 = 5 boards
Result: The largest part of the fence paints David (5 boards).