Learn Italian: Maneggiare il pacco con molta attenzione. - Handle the package with great care.

This is the Jussive Infinitive. It is used to give impersonal, general instructions, warnings, or rules. You will often see this on packaging, manuals, or public signs because it addresses anyone reading it rather than a specific 'you'.

Does maneggiare mean 'to manage'?

They share a common root (from the Latin for 'hand'), but maneggiare specifically means to physically handle or manipulate something with your hands. If you want to say 'manage' in the sense of running a business or organizing a situation, you would use the verb gestire.

Could I use an adverb like attentamente instead of con molta attenzione?

Yes, you could say molto attentamente (very carefully), but con molta attenzione (literally 'with much attention') is the most standard, natural phrasing used on Italian shipping labels and warnings. Note that molta changes to match the feminine noun attenzione.

How would I make this instruction negative, like 'Do not handle'?

You simply place non directly in front of the infinitive: Non maneggiare il pacco. As a B2 learner, you might remember that this looks exactly like the negative informal imperative (telling a friend 'don't handle'). For both general instructions and the negative informal imperative, non + infinitive is the rule!