I have 2-2-2-4 AL dyke quadruplex direct burial 600v. with AC/heater wall unit. with about 9 plugs. a small hot water heater. and 9 can lights. is a 60amp breaker big enough. Also the wire is running about 100ft from main to a subpanel
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That supply cable is nice and stout and can support more than 60A. I agree with R.M.E... Whether you'll need that depends on the size of the water heater. The can lights are of no consequence, and the deciding factor is what else you'll be plugging into the 9 sockets.
Regardless, I strongly recommend "going a bit nuts" with the subpanel size. You want a lot of extra spaces, because running out of spaces is a serious problem so easily avoided! Aim to have twice the spaces you expect to use. You figure "oh, I'll just run a table saw", 1 breaker space, then you find out you can't run a dust collector on the same circuit, +1 space. Then you get a nice deal on a 220V table saw +2 spaces, etc. etc. etc.
Also, don't get a 60A subpanel because you won't get full capacity out of your wire.
The subpanel can be larger than the feeder breaker and wire. Get at least a 100A because your wire can support it, or even a 125A if that makes sense (bigger panels also give you more bonus breakers).
You are asking us to give you a calculation for a feeder of a building and you are not providing enough information. Based on very general loads I use for rough estimates of usage. Your demand is about 57 amps if you are connecting up a 120/240V 1ph 3w panel.
You feeder conductors are large enough but I would say you need to increase you breaker up to at least a 70 amp.
The question is will it work? I don't know since we don't know the use of this building. Is any other equipment being installed, the load size of the water heater, or the VA/W of lights you are planning to install. Also the information you have given us on the heater does not include the RLA (run load amperage).