Predicting the product of bromination of acetanilide I figured the answer would be option (B) as the group attached to the benzene ring is ortho- and  para- directing.

I thought $\ce{FeBr3}$ would be used in electrophilic aromatic substitution.

However, the model answer to the question is (D).

Is this correct? If so, what makes it possible?
This is a classic $\alpha$-bromination of a carbonyl. You can achieve this with an electrophilic source of bromine like in the reaction conditions provided or something like N-bromosuccinimide.

The reason you're not getting the EAS product is because that's a much higher energy pathway since you need to temporarily break aromaticity. Given more time, heat, and bromine, you can probably get the ortho- and para- products, but you will still $\alpha$-brominate on the amide first.