There is no one-size-fits-all answer to this question, as the age at which a homeschooled child can quit school varies from state to state. In some states, homeschooled children are required to continue their education until they reach the age of 18, while in other states, they may be able to discontinue their education at an earlier age.
For more information on the specific age at which a homeschooled child can quit school in your state, it is important to consult with your state's homeschooling regulations.