The theory that the government can best stimulate the economy by businesses produce more is known as what?

The correct answer is: "supply-side economics"

Supply-side economics is a macroeconomic theory that encourages the reduction of taxes and fosters deregulation, as the manner of stimulating the total output produced by businesses and, in turn, the economy of the country as a whole.

It contrasts with macroeconomic theories that aim to stimulate aggregate demand by increasing goverment spending and, in turn, increasing taxes too (to collect the funds which are necessary to increase the expenditures).