Learn Finnish: Etsin suurta laukkua. - I am looking for a large bag.

This is adjective agreement in action! In Finnish, an adjective must match the noun it describes in both case and number. Because the verb requires the object to be in the partitive case, both suuri (large) and laukku (bag) get partitive endings, becoming suurta laukkua.

Why does the verb etsiä (to look for) require its object to be in the partitive case here?

The verb etsiä always takes a partitive object. This is because searching is an ongoing action without a guaranteed or immediate endpoint. You are in the process of looking, so you use the partitive form laukkua.

The basic word for large is suuri. Why is its partitive form suurta and not suuria?

The word suuri is an older Finnish word ending in -i. Many of these older words take the -ta or -tä ending in the partitive case instead of just adding an -a or -ä.

Why isn't the word minä (I) used at the beginning of the sentence?

In Finnish, the personal pronouns for I (minä) and you (sinä) can often be left out. The -n ending on the verb etsin already makes it perfectly clear that I am the one looking.