Leak

Get a second opinion from a different shop. Brown fluid is usually engine oil. It can leak from a cylinder head gasket, but it is far more common to be leaking from the valve cover gasket. That is the highest point on the engine. Look for the highest point you see wetness. Oil only runs down, not up, and it will run over the same area where it would run from a leaking head gasket.

Look for which fluid level is dropping over a few days. It is normal for the oil level to drop a little between oil changes, but it should not be excessive. If it is oil that is leaking, consider washing the area with a spray can of engine degreaser, then adding a bottle of dark purple dye to the oil. Search a day or two later with a black light. The dye will show up as a bright yellow stain that you can follow back to the source of the leak. Auto parts stores will have the correct dye for the fluid being tested, and those that rent or borrow tools should have a black light.