El próximo verano, Alejandro [blank] a mochilear a la montaña Cotopaxi translates to "Next summer, Alejandro [blank] backpacking to Cotopaxi Mountain. To find the correct verb, know the subject; is it plural or singular? The subject is Alejandro, one person, thus it is singular. This means the verb must also be singular. Let's look at the options.
· irá - he/she/you (formal) will go; singular
· iremos - we will go; plural
· irán - they will go; plural
· irás - you (informal) will go; singular
Clearly the correct conjugation of ir for the subject Alejandro is irá.
El próximo verano, Alejandro irá a mochilear a la montaña Cotopaxi