Can you stand on one foot with your eyes closed for one minute?

Literal

Eyes [obj-を] closed one-foot [on-で] 1-minute standing-can [Q-か].

片足で ('on one foot') uses the counter 片 ('one of a pair'). 立っていられます is the polite potential of ~ている — 'can remain standing.' A physical challenge phrased as a polite question.