。
You've gotta calm down and study.
Literal
Calmly study-not-must dame [emphasis-よ].
~なくてはダメ is a more colloquial variant of ~なくてはいけない/ならない — ダメ ('no good') stands in for いけない. Very common in spoken Japanese for casual obligation. The te-form 落ち着いて attaches to 勉強する as a manner adverbial: 'calm down and study.'