What is the proper form?

Nosotros (deber/estudiar)___ mucho esta semana.
debemos/estudiamos or debemos/estudiar

"debemos estudiar" is the correct form.

The conjugated verb "debemos" (we must; we have to) takes the infinitive "estudiar" (to study)

Note that to study is the infinitive = estudiar. If you write two conjugated verbs together, such as "debemos estudiamos" you have "we ought to/we must we study/do study/are studying. (a run-on sentence)

Sra

The correct form of the verb in the blank space is "debemos/estudiar."

To determine the correct form, you need to analyze the subject of the sentence, which is "nosotros" (meaning "we").
Since "nosotros" is a first-person plural pronoun, it requires the verb form that agrees with it. In this case, the verb form is "debemos" (which means "we must" or "we have to") because it matches the subject "nosotros."
Additionally, the infinitive verb "estudiar" is used after the verb "debemos" to indicate the action "studying." This combination forms the correct sentence: "Nosotros debemos estudiar mucho esta semana." (Translation: We must study a lot this week.)