This tiny little Weber 32/36 inlet filter sits between the inlet barb on the carb and the needle and seat assembly. This filter is usually the last line of defence for small debris prior to entering the fuel bowl. When this blocks up with particulates, the engine will run terribly - often cutting out and having issues with fuel supply and startup.
To access this filter, just remove the brass hex fitting on the underside of the 32/36 top cover and it will be sitting there lodged between the brass hex and a locating pedestal in the casting of the weber body. To replace you can easily remove the old filter and simply replace, just make sure to re-tighten the big hex.