Final answer:
A law can be passed without the President's signature if it is not signed nor vetoed within ten days, or if Congress overrides a veto with a two-thirds majority in both houses.
Step-by-step explanation:
A law can be passed without the President's signature through two methods. The first is if the President does not sign or veto a bill within ten days (not including Sundays), the bill automatically becomes law, unless Congress adjourns before the ten-day period is up, which then results in a "pocket veto."
The second method is through a Congressional override of a Presidential veto. If the President vetoes legislation, Congress can override this veto with a two-thirds majority vote in both the House of Representatives and the Senate, effectively passing the law without the need for the President's signature.