It means that you can study hard, spend your youth with you and stay with you all the time. This sentence is often used for promises between lovers. Holding your hand with your left hand means being with you, and holding a pen with your right hand means studying hard and living up to your youth. It means that you will neither waste your study youth, that is, study hard, nor forget the love between us, that is, you are always around. So holding a pen in your left hand and a pen in your right hand will not disappoint your youth. You mean you can not only study hard, but also spend your youth with you all the time.