Learn French: J'ai fini par comprendre l'astuce grâce à mon intuition. - I ended up understanding the trick thanks to my intuition.

The main verb is conjugated in the passé composé (J'ai fini), and it is followed by par and the infinitive (comprendre). Note that while English uses an -ing form ('understanding'), French always uses the infinitive after the preposition par in this structure.

Could I use à cause de instead of grâce à here?

No, because grâce à is used when the cause is positive or helpful (just like 'thanks to' in English). À cause de is used for negative or neutral causes ('because of' or 'due to'). Since understanding the trick is a positive outcome, grâce à is the correct choice.

Intuition is a feminine noun. Why do we use mon instead of ma?

This is to avoid the awkward clash of two vowel sounds. Whenever a feminine singular noun starts with a vowel or a mute H, French swaps in the masculine possessive adjectives (mon, ton, son) instead of ma, ta, sa to make the pronunciation flow smoothly.

Does l'astuce just mean 'the trick' like a magic trick?

Not quite! While a magic trick is un tour de magie, une astuce specifically means a clever trick, a life hack, a knack, or a handy tip. It implies a smart shortcut or an ingenious solution to a problem.