Learn Italian: L'assassino è il cuoco? Penso di sì. - Is the murderer the cook? I think so.

You only use the subjunctive when you follow pensare with che and a new clause with a subject and a verb (like 'I think that he is...'). Because Penso di sì is just a short phrase meaning 'I think so,' there is no second verb to put into the subjunctive!

Why do we need the word di in Penso di sì? Can I just say Penso sì?

You cannot skip the di. In Italian, verbs expressing thought, hope, or communication (like pensare, credere, sperare, or dire) must connect to sì (yes) and no (no) using the preposition di. Think of it as saying literally 'I think of yes.'

How do I say 'I don't think so' using this same structure?

You simply swap out the sì for no and say Penso di no (literally, 'I think of no'). This is much more natural and common than saying Non penso di sì.

If I wanted to reply with a full sentence using the subjunctive, how would I do it?

To say 'I think that he is the cook,' you would use che followed by the present subjunctive form of essere (to be): Penso che sia il cuoco.