Learn Italian: Spero che il contadino coltivi l'orto. - I hope that the farmer cultivates the vegetable garden.

Because the sentence starts with Spero che (I hope that). Verbs expressing hope, wishing, or uncertainty trigger the subjunctive mood in the clause that follows. Therefore, the indicative coltiva becomes the subjunctive coltivi.

Doesn't the -i ending on coltivi usually mean "you" (tu)?

In the normal present tense (indicative), yes. However, in the present subjunctive, regular -are verbs like coltivare change their endings to -i for the io, tu, and lui/lei forms. Here, coltivi represents the "he" form matching il contadino.

If coltivi is the exact same word for "I", "you", and "he/she" in the subjunctive, how do we know who is cultivating?

Here, the noun il contadino (the farmer) clears up any ambiguity. If we were using pronouns instead of a specific noun, we would likely include the pronoun to avoid confusion, such as Spero che lui coltivi l'orto (I hope that HE cultivates the vegetable garden).

Why is "vegetable garden" translated as orto rather than giardino?

In Italian, un giardino is typically an ornamental garden with grass, flowers, or decorative trees. Un orto specifically refers to a patch of land used for growing vegetables, herbs, or fruit, which fits perfectly with what a farmer would cultivate.