Small Engines (Lawn Mowers, etc.): Stihl FS66 weed eater, air filter assembly, car router

Question
Thanks in advance for answering my question.
I have a Stihl FS66 weed eater which is very hard to start when cold.  I've checked and set the gap for the spark plug.  The electrodes look fine, dry and have a whitish tint to them.  The trick I've come up with to get it started is to prime the  engine by pouring a little gas into the spark plug hole.  Once it starts and warms up I can restart it effortlessly.  However if I shut it off and let it sit for say 5 minutes I have difficulty starting it again.  Starting from a cold condition, I have to play the throttle to keep it going.  Once it warm up it idles OK.  

My research shows that the only carbs offered for the FS66 were Walbros. The first was a WT-38 p/n 4117 120 0605, the second was the WT-45 p/n 4126 120 0600, and
finally the WT-112 p/n 4132 120 0600.  

The only markings I found on the carburetor are the following:
Behind the air filter assembly:
M410
M4
On top of the carburetor:
Sthil
On the bottom of the carburetor:
83
From these markings I can not determine which carburetor is used on my FS66.  I'm hoping you can.

I hope the above information is enough to solve my problem.

Answer
I believe Walbro manufactured the carburetor for Sthil.  It more than likely only has there markings on the carburetor.

Pouring fuel into the cylinder to start the engine is usually not a good idea.  That's what a primer is usually for if your tremor has a primer be sure check the bulb for holes and a primer light.  I think what has happened is the screen inside the carburetor has become plugged.  To clean it the carburetor has to be disassembled.  While disassembled install a new car router Kit.  You will have to get it from Sthil or contact Walbro.  I know Walbro has a website.  When reinstalling the carburetor check the insulator a block for warpage.  Key insulator block goes between the carburetor and the cylinder and protects the carburetor from heat.  If the gaskets on either side of this are damage they have to be replaced.  It is a good idea to replace all caskets and O rings.  Hope this helps