In short this is very common.
Japanese is structurally built to stack words and phrases onto each other, the technical word if you want to look into it more is
a process of word formation in which morphemes, each having a relatively constant shape and meaning, are combined without fusion or morphophonemic change.
This style of grammar means that the modifying words cascade in meaning until they hit a terminal word that takes on the extra nuance provide by the preceding morphemes. This can happen in both direction in Japanese between verbs and nouns.
The eaten food.
They eat seriously.
In your sentence there are three phrases,
「好きなことをやる勇気を」- [the courage of doing things I like]
「教えてくれました」- [gave me instruction]
The middle phrase has two sub phrases but it acts as one agglutinated phrase.
「好きなことをやる」- to do the things I like
As you can see the first phrase is itself a complete sentence but that whole idea is modifying the concept of courage, giving it a context and a type or style of courage. This kinda of pattern is very common.
*note this is technically a na-adjective in English parlance but they are nearly identical to nouns in terms of this discussion. This is usually the way that nouns become adverbs in Japanese is that there are a subset of nouns that already function as adjectives and can be used as adverbs.