How and where do you adjust the synch on 1986 gsxr

I can help with this.
On the earliest models they had slide type carburettors. This is to say that the slides were actuated by the throttle cable acting on a linkage that physically lifts the slides in the carburettors. This type of carburettor has its balance(syncronization) adjusters under the caps on top of the carburettors.(the cap isn't round & has 3 screws in it)
Number three carburettor is fixed & dosn't get adjusted.

You'll have to put the bike next to a bench & attatch a long piece of fuel hose from the tank to the fuel hose on the carburettors.You can join the two pipes together using a short piece of hose that snuggly fits on the outside or inside of the two hoses. You can also join them with a suitable shirt piece of metal pipe,or what is called here in Australia a P3 barb.These are available from tool suppliers that supply air compressor hoses & fittings.
(I made a remote tank from an old lawnmower petrol tank,a long piece of hose & mounted it on a tall stand.Under it I have a tray with all my different adaptors in it.)

You adjust number 2 cylinder to the same vacume reading as number 3 cylinder first.
Now adjust number 1 cylinder to the same vacume reading as number 2 cylinder.
Next adjust number 4 cylinder to the same vacume reading as number 3 cylinder.
Recheck that they are all the same & your done.
The adjusters are of the screw & locknut(8mm)type.
You can struggle with an 8 mm ring spanner & a flat bladed screwdriver,buy an adjusting tool(genuine, or non-genuine from a bike shop) or make one.

To make one you weld a bar onto the side(at the top)of an 8mm extended quarter inch drive socket.Then find a long small screwdriver that will fit down the hole.

After you make each adjustment,stop the engine & open the throttle wide open & release a couple of times.(This seats the slide).After diong this re-start the engine & re-check your adjustment.
I place a fan blowing on the engine to help control the engine temperature as the adjustment can be a bit of a fiddle.

I prefer to use mercuary type vacume guages as they dont go out of calibration.

If you are using dial type guages check that they are all reading the same by checking them all one by one on the same cylinder.
Some Suzukis' have a pipe (covered with a black rubber stopper) at the top of each carburettor(at the front) & others have an allen screw on the cylinder in front of the carburettor manifold rubber.
If yours has the allen screw you will also need adaptors that screw into the hole once the allen screw is removed.

If you bike has diaphram type carburettors on it(you'll be able to recognise this by the top caps of the carburettors being black & roundish in shape & held in place by 4 screws), the adjusting screws are between each carburettor & are the spring loaded type.
The adjusters are located in-between each pair of carburettors visable from the top.
These are easier to adjust as there is no lock nut to struggle with & all you need to turn the adjusting screws is a long (flat or phillips)screwdriver.
Again, balance the center two first,then the left pair then the right pair.

This procedure is applicable to all in line 4 cylinder motorcycles (even most fuel injected ones.

Regards Andrew Porrelli