~ことができる
RuleVerb dictionary form + koto ga dekiru: can / be able to.
Curiosity
How do you say you "can" do something — ability or possibility?
Intuition
Literally "the act (koto) of doing — is possible (dekiru)". Turn the verb into a noun phrase with koto, then add "is possible".
Visualization
hanasu → hanasu koto → hanasu koto ga dekiru. Nominalize the verb, then dekiru.
話すdictionary form
Essence
koto ga dekiru expresses ability/possibility and is more formal and written than the potential form (hanaseru). In speech the potential form is more common.
Examples
日本語を話すことができます。
I can speak Japanese.
ここで泳ぐことができますか。
Can I swim here?
漢字を読むことができる。
I can read kanji.
Mini-quiz
"watashi wa piano o hiku___." (I can play the piano)