Your original muffler is the optional one shown on the Briggs Illustrated Parts List. Note that because of its offset shape it has to be "timed" rotationally, to clear the breather tube going to the carburetor. To make this timing possible without the muffler being loose in the thread, it has a locknut on the thread holding it screwed into the exhaust port. You have to loosen this locknut first, before you can unscrew the muffler from the port. It is a normal right hand thread. I doubt your new muffler came with a locknut - if it didn't you will need to reuse the original one. You will also need to soak the threaded part of the old muffler with Penetrene or something similar for a day or so to get it out of the exhaust port without it just breaking off and leaving you with a problem. Putting some anti-seize agent (such as Kopr-Kote) on the new thread before you screw it in, should help make it easier to remove next time. Screw the new muffler in by hand until it is firm, then undo it the minimum amount necessary to achieve the required rotational position, then tighten the locknut to hold it in that position.
Note also that your original muffler had an exhaust deflector on its outlet hole, to keep the mower operator from being in line with the exhaust blast. You may decide you need to source a deflector, depending how tolerant you are of getting blast-marks on your knees.
I understand the Briggs exhaust fittings use standard US National Pipe Taper (NPT) thread. Remember that US pipe threads, like British ones, (BSP, also known as Gas), are sized by the inside diameter of the pipe, not the outside diameter of the thread.
