Yes, you can say: Can you manage that yourself? Can you manage that by yourself? And sometimes just: Can you manage it/that? All would apply, whether the task is physical or mental, hard or easy. For example: Finishing off a big piece of cake. "You're sure you can manage that? I can eat the rest if you don't want it!" :) Taking on a work project. "Are you sure you can manage it? If not, we could ask the rest of the team to help." Lifting up a heavy object. "You can manage that by yourself? I wouldn't want you to hurt your back." In all three cases, another synonym would be "handle". "You're sure you can handle it?"

I think this is a very polite of way of asking someone if they could use some help with a task. I would typically use it for physical rather than mental tasks, though. Other things that one might say would be: - Can I help you? - Can I offer a hand with that? - Can I be of assistance? << very formal - Here, let me help you with that... - Here, let me give you a hand with that (those)... I hope this helps!