Alexander hamilton's argument that the government has the power to create a national bank is based on which part of the constitution?

Hamilton's argument was based on the "necessary and proper" clause of Article I, Section 8, of the United States Constitution.
After enumerating a number of the powers of Congress, including borrowing money, coining money, regulating commerce, etc, Section 8 of Article I closes with by saying Congress shall have power "to make all Laws which shall be necessary and proper for carrying into Execution the foregoing Powers, and all other Powers vested by this Constitution in the Government of the United States, or in any Department or Officer thereof."  
Hamilton favored a loose interpretation of the Constitution -- in other words, that the Constitution allows for anything that is not strictly forbidden in what it has expressly stated.  A national bank was not strictly listed as something Congress could establish, but there was nothing in the Constitution to prohibit it.  And the "necessary and proper" clause gave leeway to create it.