Where do the fuel lines connect after carb?

So I got my 78 kz400 a couple days ago off kijiji it's missing a few things but hey I can fix most of it. But I cannot figure out where the fuel lines connect after the carb... and I cannot find diagrams or videos or anything that make sense to me. Please help.

After the carb? Do you mean the drain hoses?

From the carburetor parts diagram at Partzilla for the 1978 KZ400-A2, there should be a fuel Tee between the carbs.
On the carb bodies kinda midway up, each carb should have a vent port --- connect tubing & leave it open to atmosphere.
The ports on the bottom of the carb float bowls are for the carb overflow/drain tubing. The tubing is usually routed behind the engine, forward of the swing arm and away from the chain & mufflers.

Kawasaki.com has the diagrams for your bike in the Owner Center section. PowerSportsWarehouse is another place.
Please note that some sites don't provide the full part numbers (bikebandit maybe?). The other sites I listed do.

The diagrams Martin mentioned are really helpful, but your best friend will be a genuine Kawasaki Factory Service Manual. They come up for sale online from time to time, and somebody here or over at the 400 forum may have an electronic version to share.

In other fuel related news, the fuel tank also hase a vent hose that should be routed to the same place that the carb vents and battery vent hose go. The petcock (fuel valve on the bottom of the tank) has two hose barbs. The smaller one (points to the rear of the bike I think) is for a vacuum hose that connects to the vacuum port on one of the carbs. The larger port (points toward the engine ?) is for the fuel line that connects to the tee Martin mentioned.

Oh yes, get a fsm.

His bike should have a manual fuel valve & I don't think there's a fuel tank vent hose.

Ok so here is the diagram that is closest to what i see on my bike without the lines connected. The t is already on my bike all that i was missing was the 4 lines coming off the carb. should my engine be starting or am i missing something?

Have you ever seen the bike run? Not starting could be any number of things.
The missing vent & overflow tubing shouldn't have anything to do with it not starting.

All 3 models from 78 - A2,B1 AND C1 have manual fuel valve/tap/petcock and No tank vent
Main fuel line from T join to tank - overflows and drain bowl tubes not necessary .
Cant quite see on my diagrams - you should have 1 Brass nipple at the front and on top of each carb - these are to use a x 2 manometer (Carb Sync) - your models are slightly different to here in carb setup - do you have caps on the brass nipples i mentioned or rubber tubes coming off them ?

Instead of the typical vacuum nipples, I think his carburetors have vac screw plugs in the vac ports.
I'd guess he'd need to remove the screw plugs & attach vac nipples, then the carb sync tool. ???

Martin - same as my old 900 Rol'Dor with the screw in plugs for sync (possibly). None of the diagrams show these unfortunately .
MR Blue i have a FSM PDF, but unfortunately it is for KH 400 (and KH 250) from 1972 - 1976 so Mikuni carbs but it may be of some use till you get the correct one - i can put it on Drop Box for you if you like. 17.1 Meg .

The carb parts diagram for his 78 400-A2 shows the screw plugs but doesn't identify them as vacuum plugs which I think they are. not really sure.