1.conjugate the verb preferir. 2.what takes place in the conjugation that makes this verb a stem-changing verb?

We will use in this problem two tenses. The simple present and the preterite. So:

Simple present:

The simple present tense is used to talk about habitual actions or routines. So conjugations of the verb preferir using subject pronouns are the following:

Yo prefiero

Tú prefieres

Él/ella prefiere

Nosotros preferimos

Ustedes prefieren

Ellos/ellas prefieren

Preterite tense:

The preterite tense is used to describe actions that took place or were completed at a certain point in the past So conjugations of the verb preferir using subject pronouns are the following:

Yo preferí

Tú preferiste

Él/ella prefirió

Nosotros preferimos

Ustedes prefirieron

Ellos/ellas prefirieron

What makes the verb preferir to be a stem-changing verb is that this is an irregular verb. For this type of verbs, you must learn by heart conjugations because there is no any rule for this type of verbs that you may follow. This is what makes this language to be difficult, the vast conjugation of verbs.