Which hydrogen atom would be most easily extracted by a bromine atom?

The proton which is easily abstracted in 1-Benzyl-3-propylbenzene is the proton which is present on carbon atom in between two phenyl rings, or the central carbon which is shared by two benzene rings.

This easy abstraction of proton is due to its high acidity. Remember those species are always more acidic whose conjugate base is stable. Like the acidity of carboxylic acid is due to stability of the acetate ion.

In our case the stability of conjugate base arises due to stability of negative ion due to resonance. As shown below, the negative charge can delocalize on both rings.

I have shown the resonance of negative ion on both Phenyl rings with Blue and Pink colors.