To find the number of tiles required to cover the path, we need to calculate the area of the path.

The length of the garden including the path is 24 m + 2(1 m) = 26 m. The width of the garden including the path is 14 m + 2(1 m) = 16 m.

The area of the path is (26 m) * (16 m) - (24 m) * (14 m) = 416 m².

Since each tile has an area of (20 cm) * (20 cm) = 400 cm², we need to convert the area of the path to square centimeters.

416 m² * (100 cm/1 m) * (100 cm/1 m) = 4160000 cm².

Now, we can calculate the number of tiles required:

4160000 cm² / 400 cm² = 10400 tiles.

Therefore, we need 10400 tiles to cover the path.