Learn Croatian: Brodogradnja je ovdje bila jako važna prije mnogo godina. - Shipbuilding was very important here many years ago.

It is made by combining the nouns brod (ship) and gradnja (building or construction). The -o- in the middle is an interfix—a connecting vowel used to glue the two roots together. This is a very standard way to form compound nouns in Croatian.

Since brodogradnja is made of two different words, how do we know its gender to use feminine forms like bila and važna?

In Croatian compound nouns, the gender and declension are always determined by the second word in the compound. Because gradnja is a feminine noun ending in -a, the entire compound brodogradnja is feminine, requiring the feminine agreement in bila and važna.

Isn't godina the singular form for 'year'? Why is it used after mnogo here?

Words denoting quantity, like mnogo (many/a lot), require the noun that follows to be in the genitive case. Here, godina is actually the genitive plural form. For the noun godina, the genitive plural happens to look exactly identical to the nominative singular.

Why does the sentence use prije to mean 'ago' in the phrase prije mnogo godina?