96 rectangles.
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In a 4 by 4 grid, there are 16 squares (1x1 squares), 9 rectangles that are 2x1, 6 rectangles that are 3x1, 4 rectangles that are 2x2, and 1 rectangle that is 4x4. Therefore, in total, there are 16 squares and 20 rectangles in a 4 by 4 grid.
45, including those whose sides run at an angle to the grid lines.
It is not possible to answer in terms of a grid that cannot be seen, but a normal grid of 2 squares x 2 squares will have 5 squares.