After a troubled teen girl is caught vandalizing state property, she is ordered to spend 6 months in juvenile detention center; where she falls in love with the, married, faculty art teacher.

The logline doesn't say the teacher falls in love with her. Only that she falls in love with him. There is no hint of complications that follow from her crush, the risk, the perils. What is at stake because of her crush?

I'm not sure it needs to mention the vandalizing? Sure there's a possible link between her "graffiti" and the "art" teacher... but it could just start:

While serving six months in juvie...

It is afterall a "forbidden love" story, yes? Give us a hint in the logline wether it's about the courting and seduction... or the deceit of trying to get away with it behind everyone's back...

I'm not very good with the rewording, but I can help with the punctuation and grammar.
Spell out the word six.
...six months in a juvenile... -- add the word 'a' between 'in' and 'juvenile.'
Get rid of the semicolon after 'center' and replace it with a comma.
Replace the word 'the' after 'in love with,' with the word 'a.'
Get rid of both of the commas on either side of the word 'married.'
Best of luck to you!