A projector lens projects an image from a 6.35 cm wide LCD screen onto a screen 3.25 m wide. If the focal length of the projector lens is 13.8 cm, the screen
must be how far from the projector

For any given projector, the width of the image (W) relative to the throw distance (D) is know as the throw ratio D/W or distance over width. So for example, the most common projector throw ratio is 2.0. This means that for each foot of image width, the projector needs to be 2 feet away or D/W = 2/1 = 2.0.

i wanna say it’s between b and d, leaning more towards b.

t = 1/400 h   ⇔ 0.0025 h ⇔ 9s ⇔ 0.15 m

any of the answers are correct.