Final answer:
Richard Henry Lee's resolution sought the colonies' independence from Britain, not more authority for England, so the statement is false. John Locke's original constitution for Carolina was true but didn't meet the colony's needs. It's true that colonial governors could veto legislation of colonial assemblies.
Step-by-step explanation:
Richard Henry Lee wrote a resolution that would allow England more authority over the colonists. This statement is False. Richard Henry Lee is actually known for the opposite; he proposed the Lee Resolution, which was an act of the Second Continental Congress calling for the colonies' independence from Great Britain. This resolution led to the Declaration of Independence and the establishment of the United States as an independent nation.
The statement regarding John Locke is True; Locke did indeed write the original constitution for Carolina, known as the Fundamental Constitutions of Carolina. However, it turned out to be impractical and was not fully adopted by the colony.
The assertion about colonial governors having the right to veto legislation is also True. Colonial governors had the power to veto laws passed by colonial assemblies, reflecting the control that the British government had over colonial legislative processes.