Hot and cold come out of the wrong sides of the handle. On a Moen single handle faucet this is almost always an orientation problem with the cartridge, not a plumbing problem, and the fix depends on which cartridge you have.
Not sure this is your faucet? See how to identify your Moen cartridge without a model number, or how to find your brand and model.
1225 cartridge (sink faucets before 2009, Standard and Moentrol showers)
Remove the handle so you can see the brass stem. Grip the stem with pliers and rotate it 180 degrees. Reinstall the handle and test. The cartridge itself stays in the valve. The small notch on the stem should face the front of the faucet when hot is on the left, and the back when supplies are crossed.
1222 Posi-Temp (rotate-only shower handles)
Shut off the water, remove the handle, limit stop, and retaining clip, pull the cartridge, rotate the entire cartridge 180 degrees so the H and C tab points down instead of up, and reinstall. Full steps are in the 1222 guide.
1255 cartridge (sink faucets 2009 and later)
The 1255 cannot be rotated to fix this. Shut off the stops under the sink and swap the hot and cold supply lines at the faucet connections.
Why it happens
Three common reasons: the cartridge was installed 180 degrees off during a repair, the supply lines under the sink were connected backwards during installation, or in a shower the valve body was installed upside down. The fixes above work regardless of the cause.