To dissect a 6x6 square into 4 equal-size squares and 4 equal-size pentagons using straight lines, you can follow these steps:

1. Start with a 6x6 square.
2. Draw two horizontal lines across the square, dividing it into three equal horizontal strips, each 2 units high.
3. Draw two vertical lines down the square, dividing it into three equal vertical strips, each 2 units wide.
4. This gives you 9 smaller squares, each 2x2 units.

To form the pentagons and equal-size squares:

1. Consider the central square and the four corner squares.
2. Each of the four corner squares will remain a square (4 squares in total).
3. From the central square, draw lines from its corners to the midpoints of the four adjacent squares' sides.

Here is a step-by-step breakdown:

1. Draw the square grid as described above:

   0   2   4   6
   +---+---+---+
   |   |   |   |
   +---+---+---+ 2
   |   |   |   |
   +---+---+---+ 4
   |   |   |   |
   +---+---+---+