What is this and how should the vacuum line be routed?

I'm guessing that's a Sammy, but details of the engine and model would really help.

Yeah its an 87 samurai 1.3 I bought it a month or so ago and just finished rebuilding the engine. It sounds really good but I'm struggling to get it run smoothly. I put all the vacuum lines back where I found them but according to acks faqs the line that's on this diaphram should go to the thermal valve on my air cleaner whitch doesn't have anything hooked up to it. I'm in the prosses of rerouting and testing all the vacuum stuff but can't find any info on what that does or where to hook it.

It sounds like your already on Acks Faq, are you using this page?

http://www.acksfaq.com/Samvacuumlines.htm

That looks like the choke piston, which I think attaches to a vacumn solenoid on the firewall, I don't know as I have an SJ-410 with a manual choke.  You can see it in two of the last three pictures on the faq page.

It looks like on yours it is routing down and back into the intake.  It could be that your choke is getting stuck open.

Yeah that's the page I'm useing i think the choke is on the other side of the carb. This one is connected to the throttle linkage on the bottom right under the idle screw

Is there a second tube on top of that then?  I couldn't tell from your picture.  If so then that would be the secondary actuator valve.  It should go to a T...

What is this and how should the vacuum line be routed?

That is the idle up for the AC.  The hose for that comes from, or goes to, a solenoid that is mounted on the firewall (yours doesn't have that solenoid on the firewall though).  Don't worry about hooking anything to it, since you don't have AC.  You can even remove it and remove the stuff from the carb shaft, if you want.
The AC idle up diaphragm is not shown on the vacuum diagram you are looking at.
The hose that you have connected to it now is supposed to go to the rear port on the airbox lid.

Did you check to see if all the vacuum diaphragms are good?  The choke pull off is opposite of this on the other side of the carb.....they are usually bad.  The HIC is a lot of times bad too (it is towards the front of the carb on the drivers side).  The idle up (it is under the choke pull off diaphragm on the drivers side of the carb) is usually good.  If any of these are not working correctly, then it can make the engine run crappy.

Ok that makes a lot of sense. I knew that hose needed to go to the air cleaner (that was a pic of the engine before I tore it apart) but I couldn't figure out what hooked up to it. Thanks a bunch I will check those other components you mentioned to get it running good for now. But I think I'm going for a harley side draft. Thanks again