Question

How do taxes support the economy??

Answer 1

Not sure what you exactly mean, as you can find different cases for it. If you ever studied Keynesian economics, you would see that in times of inflation, the government would raise taxes so that, in times of recession, they can pump money back in the economy through jobs such as road/bridge building.
Or you can be general and say taxes are used for social programs such as trains, health care (if you have it in your country), and education