。
Her eyes shone with happiness.
Literal
She [topic-は] happy-seemingly eyes [object-を] was-making-shine.
目を輝かせる is a vivid causative collocation: 輝く ('to shine') becomes 輝かせる in causative — 'to make shine.' The literal subject 'she' makes her eyes shine — Japanese frames the action as the speaker controlling the body part, even when the actual cause is emotional. 幸福そうに ('looking happily, in a happy manner') uses the visual evidential ~そう adverbially with に. The whole phrase paints a quietly cinematic image — eyes lighting up with feeling.