。
She went to Germany with the goal of studying music.
Literal
She [topic-は] music [object-を] study purpose [with-で] Germany [to-へ] went.
~目的で ('with the purpose of') is one of several Japanese ways to express purpose, this one explicitly naming intention via the noun 目的 ('aim, goal, purpose'). It feels slightly more deliberate and stated-in-advance than the smoother ~ために. Germany has long been a destination for Japanese students of classical music — particularly for piano, lieder, and the German romantic tradition — with conservatories in Berlin, Munich, and Hannover drawing international students.