[lrhyner]

I know when in the presence of peroxides, the Br will be added anti-Markovnikov, but I am not sure what that means

[zhangcarlin]

your teacher asks you to draw the structures of X, Y, Z

[discodermolide]

I know when in the presence of peroxides, the Br will be added anti-Markovnikov, but I am not sure what that means

If you are not sure what "it" means then you should not really quote it.
Try Googling the word Markovnikov and see what you come up with. Then have another go at the problem.

[Babcock_Hall]

There was a previous thread where a similar question came up:  http://www.chemicalforums.com/index.php?topic=62080.msg221875#msg221875

[PhDoc]

I would suggest being careful with that term "anti-Markovnikov."

There are a few definitions of Markovnikov's Rule, however the "true" one will lead you to a better understanding of mechanistic organic chemistry.

Simply stated, Markovnikov's Rule holds that "stuff" adds to alkenes (and alkynes) to generate the most stable intermediate. The "stuff" can lead to carbocation or radical intermediates, or may proceed via a concerted transition state with elements having seemingly unexpected electrophilic or nucleophilic properties.

Present this definition to your professor, and then ask him/her if Markovnikov's rule is ever really violated.

[orgopete]

Since X reacts with HBr with and without peroxide to give two different products, what must X be? If the peroxide addition is anti-Markovnikov addition, then what must Y be? (X must be an alkene.)