The problem is whether you can understand her English.

Literal

Problem [topic-は] you [subj-が] her [poss-の] English [obj-を] can-understand [whether-かどうか] [copula-だ].

理解できる is the potential form of 理解する ('understand'). 君 is an informal second-person pronoun, used between male peers or by a superior to a subordinate.