How to clean white grout in terrazzo?

They sell grout cleaner at Home Depot. Use that stuff and a lot of elbow grease. Then you will need to purchase whats called grout sealer. You put that on the grout. Two coats should do it and after that its easier to clean in the future.

Try a mix of hydrogen peroxide and water, 1 hy to 3 water to start, stronger if needed. Basically a bleach, we use a toothbrush to apply and scrub with. Then as buster said, seal it for future easier cleaning. Should be sealed every few years to keep a good barrier.