Please supply a bit more information.
I see a hand-pull rope; and maybe an electric starter?
You really want to verify the engine capability on a specification fuel to rule out an engine problem.
THis can be done with bottled propane gas.
Put the propane bottle into a bucket of warm (NOT HOT!) water to insure a good from liquid-to-vapor supply.
The propane tip supply must be able to supply an adequate amount of propane gas. Small engines like this one I’ve been able to supply through a stock propane torch nozzle. Bigger engines had to go with a higher flow supply nozzle.
This engine at stopped governor default to a wide open throttle position. A gasoline carburetor with it’s internal venturi will still be able to low pressure create and suck/atomize the gasoline.
On a T-mixer replacement the wide open throttle not create enough intake suction. to pull in enough fuel
You can hand override the governor to throttle lever arm to close down some that throttle under cranking. Or build a choke flap onto the air-in side of the T-mixer.
Otherwise you will over-air run too fuel lean on cranking starting up; woodgas or gaseous propane.
Fuel lean mixed do cause intake back fires.
Regards on your efforts so far
Do realize all of this advice is to get your actual engine “workable” tested just to start-up and idle run on a know spec grade of fuel.
Engine grade testing your produced woodgas is a whole 'nother concern. Spark ignitable flare as a first step.
As Ben’s book specifies this engine loading is too small to demand-draw heat load that gasifier for best woodgas making performance. About 1/2 too small. You will have to work the fuel bits sizing and dryness then as a driven-needs primary concern.
See another members topic here about outside made charcoal fueling his Ben’s Book woodgasifier for his too small of engines. No conclusion success reported yet. But the DOW members exchanges to him will be instructive.
Note to all. Ben Peterson is a guy I’ve shoulder to shoulder worked with for a number of years.
His Book system is greatly simplified just to make it widest possible user build-able out of readily available materials. Get you up to making woodgas. Using woodgas in as wide as possible of personally owned&used engine applications. Your actual 'gitter-done using then. With your own actual local sourced wood fuel inputs as your training teacher.
He HAS made producer-gas to build-plastic/build a liquid fuel base feedstocks gasifiers. And sold this. Only one that I know of. The willing to shell out $50K are few-to-none.
He HAS made up two different vehicle systems. One sold. Big. Big legal problems here in WA State doing past one quietly used for personal use.
He has made dedicated gasifier systems for wood pellets, woodchips, charcoal to exclusively fuelgas power small single cylinder electrical generator engines. Sold many in diffident versions and configurations. Used as designed - ok to great! Not on rubber tire chunks, urban mixed plastics wastes, and paper shreds!! Not on forest floor duff full of fir, pine needles, leafs, and shits(manures)!!
You using the right tool for the best purpose is YOUR choice. When the screwdriver you grab make’s a piss-poor hammer . . . who’s fault is that, eh?
This users wrong-choice try-forcing has driven both Jim Mason (APL) and Matt Ryder (Thrive Off Grid) nuts on many of their gasifier systems made-up and sold/deployed too.
I hate that serial flow single tube cooler too.
I have a BenP multi-parallel vertical tube cooler with rectangular upper and lower manifold boxes he made in about 2009 for compact usages. Stationary it need a fan to cool properly.
Ha! As I’ve said I can gas-cool/wash and condensate collect cool as well with a horizontal sloped 20 feet of old 4 inch ID cast iron soil (toilet drain) pipe. No fan. Just thermal air movement. And safely heat a work space with that. Just big, long. and cursed heavy. But easy clean&swab out with end caps.