First, what testing has been done to determine the controller is the problem? A complete list of symptoms, plus a list of tests and their results, will help us help you be sure that's what is wrong, or suggest other tests that can find the problem.
As for controllers, generally most of them look about like that; at a guess it's probably a 9 or 12FET but beyond that couldn't say much else. Some may not have paper labels but instead are laser engraved on one side; you might check for that if you can. Connectors vary widely. It's likely that you'll end up having to figure out the wiring of your existing controller by tracing wires from it to everything it connects to, then cutting and splicing the new controller into that wiring (or changing the connectors on the other things to match the new controller, or replacing those other things with new ones that come in a kit with the new controller).
Is it a throttle-only system, or does it also operate by pedals? (PAS)
Does it have a display? (if so, this will probably have to be changed to the one that comes in a kit with the controller)
With no info on the controller, we'll need to know any details of the battery and motor that you have, and the below info will also help us figure out what you need.
What is the bike used for? How is it ridden, and under what conditions on what terrain, etc., and what is the total system weight including yours and anything that is carried on it, and how far do you ride it each time? Knowing those things will help us make sure you get a controller that will do the job you need it to do, if the first one failed because it couldn't.
What voltage is the battery, and how many Ah or Wh is it, and what is it's A or Amp rating (or C-rating if it has one, along with it's capacity in Ah). Note that A and Ah are completely different things, so be sure to note the right numbers with the right abbreviation. If there are no labels and there is no other info, then does the charger have a label with any info? If not, you'll need a voltmeter to do some measurements we can give instructions for, once you post some pics of the battery connectors. If the charger has a label with enough info, we can make some rough guessesabout battery capacity based on how long it takes you to run the battery to empty (if you normally do), given the conditions / etc above, and how long it then takes to recharge it afterward.
What motor does it have? If it doesn't have any labels, good clear pictures of both sides and the space between the spokes including any engravings or logos may help us at least guess what it is.
