Laundry faucets like this are easy and cheap to fix. If it’s dripping from the spout, you need a new faucet washer. And if water is leaking around the handle, the rubber O-ring around the valve stem is bad. But since you have to take out the valve stem for either repair, and the fix is simple, we recommend replacing both the hot and cold washers and the O-rings while the faucet is apart. Remember to turn off the water and purge the pressure before you start. If you’re lucky, there’ll be a separate shutoff for the laundry room. Otherwise, you’ll have to shut off the water to the whole house by closing the main valve.
Photos 1 and 2 show how to do the repair. After you’ve removed the valve stems, take them to the hardware store. You’ll find drawers full of faucet washers and O-rings. Just find washers that will fit snugly in the recess, and matching O-rings. If you damaged the screw that holds the washer on when you removed it, buy new brass screws. Now simply reassemble everything in the reverse order. No more drips!