die Möglichkeit
opportunity
An opportunity or chance to do something.
Haben wir die Möglichkeit, das Projekt noch zu ändern?
Do we have the opportunity to still change the project?

possibility
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opportunity
An opportunity or chance to do something.
Haben wir die Möglichkeit, das Projekt noch zu ändern?
Do we have the opportunity to still change the project?

The word 'Möglichkeit' (possibility) is derived from the adjective 'möglich' (possible). The ending '-keit' is a typical way to form nouns from adjectives that describe a quality or state.
Es ist möglich, das Ticket online zu buchen.
It is possible to book the ticket online.
'Möglichkeit' (possibility) is very often used with an infinitive construction. The pattern is: 'die Möglichkeit haben/bieten/geben, etwas zu tun' (to have/offer/give the possibility to do something). The verb at the end of the sentence is then in the infinitive with 'zu'.
Ich hatte noch nicht die Möglichkeit, mit ihm zu sprechen.
I have not yet had the opportunity to speak with him.
When 'Möglichkeit' (opportunity) describes a chance, it is often combined with certain verbs. Typical phrases are 'eine Möglichkeit nutzen' (to use an opportunity), 'eine Möglichkeit ergreifen' (to seize an opportunity), or 'eine Möglichkeit verpassen' (to miss an opportunity).
Du solltest diese einmalige Möglichkeit ergreifen und dich bewerben.
You should seize this unique opportunity and apply.
When several options are involved, 'Möglichkeit' (option) is often in the plural and accompanied by words like 'verschiedene' (various), 'mehrere' (several), or 'zwei' (two). This is how you can tell that alternatives are meant.
Wir haben verschiedene Möglichkeiten, um nach Berlin zu reisen.
We have various options for traveling to Berlin.
In the meaning of 'resources', the word is almost always used in the plural. An adjective usually specifies what kind of means are meant, e.g. 'finanzielle Möglichkeiten' (financial means) or 'persönliche Möglichkeiten' (personal resources).
Die Renovierung übersteigt unsere finanziellen Möglichkeiten.
The renovation is beyond our financial means.
choice / election
'die Wahl' and 'die Möglichkeit' both have to do with options. 'die Wahl' emphasizes that you are deciding between several things or that there is a selection to choose from. 'die Möglichkeit' can simply be an opportunity or a possible option, even if you are not actively deciding yet. Learners often confuse the words because both can fit when talking about alternatives. In practical terms: if the focus is on deciding, 'die Wahl' fits. If it is about an opportunity or option, 'die Möglichkeit' fits.

Mein Nachbar hat die Möglichkeit, seine Kinder früher von der Schule abzuholen.
My neighbor has the opportunity to pick up his children from school earlier.
Im Restaurant habt ihr die Wahl zwischen Fisch, Pasta und Salat.
At the restaurant, you have the choice between fish, pasta, and salad.