capable
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to be capable
To have the ability or possibility to do something; to be able to.
Nach seiner Verletzung war er nicht imstande, die Treppe allein zu steigen.
After his injury, he was not capable of climbing the stairs alone.
The word 'imstande' (capable) is almost always used in the fixed phrase 'imstande sein' (to be capable). It is followed by an infinitive construction with 'zu', which describes what someone can do.
Ich bin nicht imstande, dieses schwere Paket allein zu tragen.
I am not capable of carrying this heavy package alone.
'Imstande' is a merged spelling of the old expression 'im Stande'. It literally means that one is 'in the state' or 'in the condition' to do something. This origin can help with understanding.
Der Patient war endlich wieder imstande, selbstständig zu essen.
The patient was finally capable of eating independently again.
The phrase 'imstande sein' (to be capable) belongs more to written language or a more formal style. It often sounds somewhat elevated.
Das Unternehmen ist nicht imstande, die geforderten Löhne zu zahlen.
The company is not capable of paying the requested wages.
to be able to
'können' and 'imstande sein' can both express that someone has the ability or possibility to do something. 'können' is the normal and very common verb in everyday language. It fits abilities, opportunities, and sometimes also permission. 'imstande sein' sounds more formal and puts stronger emphasis on whether someone is really capable of managing something. Learners may confuse the words because they often have similar meanings. In conversations, you usually use 'können'. 'imstande sein' fits better when you want to especially emphasize an ability or strength.
Nach der langen Krankheit war sie noch nicht imstande, allein einzukaufen.
After the long illness, she was not yet capable of going shopping on her own.
Noah kann heute wegen des Trainings nicht zum Termin kommen.
Noah cannot come to the appointment today because of training.