craftsman LTX 1000 model 422707 type 1208 02 code 87120312 twin 2 18hp

You mean, carb as in carburetor? Sounds like a problem with the fuel line. Is there a shut-off valve on it? Is it open? Could the line be clogged? See if the inliet screen blocked or clogged, disconnect the screen from the engine and blow with compressed air. Also check the gas cap for air vents that should not be blocked. Can also be the carburetor itself. Briggs & Stratton sells  a replacement kit. Looks like it's part # 693480

Also, more support for your engine is here :