The potential of する. Expresses ability with a noun-skill ('can do X'), and also 'to be finished/ready' or 'to come into being'.
[Noun (skill/thing)] + が + できる / できます
私は英語ができます。
Watashi wa eigo ga dekimasu.
I can speak English.
英語 (English) + が + できます — the noun-skill takes が; no need for 話す
晩ご飯ができた!
Bangohan ga dekita!
Dinner is ready!
できた here = 'is finished / ready'
新しい店ができました。
Atarashii mise ga dekimashita.
A new store has opened.
できました here = 'came into being / was built'
• To say you can do an ACTION (a verb), you must first turn the verb into a noun with 〜ことができる (dictionary form + ことができる): 泳ぐことができる (I can swim). • The thing you 'can do' takes が, not を.
The JLPT rarely asks whether you recognise a pattern — it asks which of several similar patterns fits. These are the ones できます is tested against.
The potential form conjugates the verb itself (泳げる); できる expresses ability with a noun (水泳ができる) or via ことができる.
ことができる is the fuller, slightly more formal way to say 'can [verb]'; the plain potential form is more common in speech.
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