Need help: engine turns off on it's own

adding to what fishbreath was mentioning. check all vacuum hoses. be sure the carburetor is tight to the intake manifold. be sure the manifold is tight to the head. LIke fishbreath said, the power brake booster may simply have the hose off or damaged.. A

n easy way to identify a vacuum leak.

First of all you should do this while the car is not too heated up so the exhaust manifolds are not all hot as heck. .. I would have a fire extinguisher present for the far off chance you ignite something.. I have done this a hundred times with no issue, so the chance of fire is slim to none..

While the car is running, spray a little mist / burst of wd-40 or spray lube (you can use starter fluid but be careful as it may want to ignite if it hits a hot exhaust manifold)
at various locations such as base of the carb where it mounts to the intake, where the intake mounts to the head, around the vacuum hoses that run round the under hood area.
you want to have the car running while doing this, close to idle as possible and at a steady rpm. If there is a vacuum leak it will suck the atomized spray lube thru it down into the engine which will rev up the engine noticeably, due to the air and "fuel" (spray lube) sucked thru the vacume leak.