Learn Hardcore German: Diese Möglichkeit wird von meinem Bruder sofort genutzt. - This possibility is used immediately by my brother.

The speaker wants to emphasize diese Möglichkeit (this opportunity) rather than the person who uses it. In German (as in English), the passive voice shifts focus from the agent (the doer) to the patient (the thing acted upon).

How do you form the passive voice in German?

You use a form of werden plus the past participle of the main verb. Here, wird (3rd person singular of werden) combines with genutzt (past participle of nutzen) to create the process-passive: wird genutzt.

Why is the agent introduced by von meinem Bruder? Could you use another preposition?

In German the most common way to name the agent in a passive sentence is with von + dative. Alternative prepositions like durch also exist but are less usual for people as agents (they often emphasize means rather than the doer). So we use von meinem Bruder, with Bruder in the dative case.

Why is it meinem Bruder and not meinen Bruder?

The preposition von always takes the dative case. The dative singular masculine form of mein Bruder is meinem Bruder (not meinen).

Why is it diese Möglichkeit and not dieser Möglichkeit?

Möglichkeit is a feminine noun. In the passive, it becomes the grammatical subject and thus takes the nominative case. The nominative feminine singular demonstrative is diese, so we write diese Möglichkeit.

Why is sofort placed after von meinem Bruder? Can you move it?

In a German main clause the finite verb (wird) occupies the second position. Everything else fills the “middle field.” Adverbs like sofort can appear in different positions within that field for emphasis or style. You could say:

Sofort wird diese Möglichkeit von meinem Bruder genutzt. (emphasis on immediate action)
Diese Möglichkeit wird sofort von meinem Bruder genutzt. (neutral)
Diese Möglichkeit wird von meinem Bruder sofort genutzt. (emphasis on who acts immediately)

What is the difference between Vorgangspassiv and Zustandspassiv?

Vorgangspassiv (action-passive) describes an ongoing or happening action. It uses werden
- past participle, as in wird genutzt.
Zustandspassiv (state-passive) describes a resulting state and uses sein
- past participle, e.g. ist genutzt (is used/remains used).

What would the active version of this sentence be?

In active voice the agent becomes the subject and the patient the direct object. The sentence is:
Mein Bruder nutzt diese Möglichkeit sofort.