How can I illustrate antimarkovnikov's rule by the addition of hydrogen bromide to propene in the presence of benzoyl peroxide?

You write the mechanism for the reaction.

This is a free radical reaction, so it has initiation, propagation, and termination steps.

Initiation

The chain is initiated by free radicals produced by cleavage of an ##"O-O"## bond in the benzoyl peroxide.

The benzoyl radicals extract a hydrogen atom from an ##"HBr"## molecule to produce bromine radicals.

##"PhCOO·" + "H-Br" →"PhCOOH" + "·Br"##

Propagation

The bromine radical adds to the propene to form the more stable 2° radical.

The 2° radical reacts with another HBr molecule to produce 1-bromopropane and a bromine radical to continue the process.

Termination

Eventually two free radicals hit each other and produce a molecule of some sort.

##"Br·" + "·Br" → "Br"_2##

##"CH"_3"-" stackrel(·)("C")"H-CH"_2 "-Br" + "·Br" → "CH"_3"-CHBr-CH"_2"-Br"##

##"2CH"_3"-" stackrel(·)("C")"H-CH"_2 "-Br" → "Br-CH"_2"-CH(CH"_3")-CH(CH"_3")-CH"_2"-Br"##

The process stops here because no new free radicals are formed.