Learn Spanish (Spain): Espero que ella alcance la caja.

This is a spelling rule in Spanish to keep the pronunciation consistent. The verb is alcanzar. In Spanish spelling rules, we generally do not write ze or zi. Instead, when the present subjunctive ending adds an e, the z must change to a c. Therefore, it becomes alcance instead of alcanze.

Why is the verb in the subjunctive mood (alcance) rather than the normal present tense (alcanza)?

The phrase espero que (I hope that) expresses a wish or desire. In Spanish, when you express a hope or desire about what someone else does, it always triggers the subjunctive mood for the second verb.

Could I drop the word ella and just say Espero que alcance la caja?

Yes, you can drop it, but it might be ambiguous here. In the present subjunctive, the forms for yo, él, ella, and usted are exactly the same (alcance). Including ella makes it perfectly clear that you mean 'she reaches' and not 'I reach' or 'he reaches'.

Can alcanzar be used for reaching things other than physical objects like la caja?

Absolutely! While here it means physically stretching to grab a box, alcanzar is also commonly used to mean reaching a goal (alcanzar una meta), reaching a certain temperature, or catching up to someone who is walking ahead of you.