Apoint source of light illuminates an aperture 4.00m away. a 18.0 cm -wide bright patch of light appears on a screen 2.00m behind the aperture.
i have been trying to use the equation w=(2*wavelength*distance)/aperature width. however, i am not given wavelength and the type of light is not specified. also, does the source of light being 4.00m away from the aperature even matter?

This problem is solved by trigonometric ratios. You do not need to use your physics knowledge about wavelengths.

You can draw two similar triangles is which the ratio of the length of the bright patch to the distance from the source of light is equal to the ratio of the length of the aperture to its distance to the source of light. This is:

18.0 cm / (4m + 2m) = x / 4m =>  x = [4/6]*18.0cm = 12.0 cm.

12.0 cm