Learn Hardcore Finnish: Tilasto näyttää myynnin kasvun. - The statistic shows the growth of sales.

Finnish has no articles. Context or additional words (like tämä for “this”) tell you whether it’s definite or indefinite. So tilasto can mean either “a statistic” or “the statistic,” depending on context.

What are the grammatical roles and cases of tilasto and näyttää?

tilasto is the subject in the nominative singular.
näyttää is the third-person-singular present tense of the transitive verb näyttää (“to show”).

Why is myynnin in the genitive case?

myynnin is the genitive form of myynti (“sales”). It marks possession: myynnin kasvun literally means “the growth of sales.”

Why does kasvu take -n (why is it written kasvun)? Is that genitive or something else?

Here kasvun is the accusative (direct object) of näyttää. In Finnish, a singular object viewed as a whole uses the accusative, which has the same form as the genitive in singular.

When would you use the partitive kasvua instead of kasvun?