
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?

option
One of several conceivable options or alternatives.
Es gibt mehrere Möglichkeiten, dieses Problem zu lösen.
There are several options for solving this problem.

means / resources
The entirety of the personal or financial means and resources available to someone. Often used in the plural.
Ein Hauskauf übersteigt im Moment unsere finanziellen Möglichkeiten.
Buying a house is beyond our financial means at the moment.
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.
chance / opportunity
Both words refer to an option to do something specific. „Möglichkeit“ neutrally describes the fact that an action is open to someone, while „Chance“ additionally emphasizes a favorable prospect of achieving a desired result. If you are talking only about what is possible, „Möglichkeit“ is suitable; when there is a positive prospect of success, „Chance“ is more appropriate.

Mit diesem Kurs habe ich die Möglichkeit, die Prüfung noch zu bestehen.
With this course, I have the option of still passing the exam.
Mit diesem Kurs habe ich eine gute Chance, die Prüfung noch zu bestehen.
With this course, I have a good chance of still passing the exam.