You can say both, but your emphasis will be different depending on which tense you use. If you use the present perfect continuous (I have been studying it), then the implication is that over the last six months, you had been studying on a regular basis (such as daily, weekly, or some other regular interval) is much stronger than using the present perfect (I have studied it). With the present perfect, as long as the total time adds up to (in your example) six months, you are making a true statement. So you could have studied, in 2012, in January, March, April, May, June, and September (if you use the present perfect).

"I HAVE BEEN STUDYING it for 6 months"means "I have studyed it for 6 months AND I will continue to study it" . If someone says "I have been in love with u for ....." It probably means the relation is going to end :)

we usually use the verb had when we finish doing some thing and have started another thing

if you still studing english you have to choose present perfect continuous...