my honda hht35s will not run when give it gas dies starts fine so I felt that maybe was carburetor so went bought new one and new filter in the tank washed tank out with high test premium gas filled up tank with premium gas new air filter checked screen in muffler looks brand new checked plug looks good what am I missing there are no adjustments on carburetor other than throttle ajustment

Take muffler off and look at the exhaust ports.
Premium gas bad , need low octane.
Higher octane will run to hot and score cylinder.
Check fuel lines and make sure there are no cracks.
Could be a cylinder gasket leak.

Hi,
Honda trimmers are OHV four strokes and as such are prone to need valves adjustments at times. The adjustment clearance is very small and sensitive. Some models were also prone to rocker arm wear, especially if the adjustment did not seem to "last." Arm replacement is the only way out there, and doo check the studs they mount to at the same time.
Peace,
Clarke