Learn Finnish: Äiti kutsuu sinut tänne.

sinä is the subject form for "you" (the person doing the action). In this sentence, "you" are the target (direct object) of the invitation. For personal pronouns, Finnish uses a special accusative form ending in -t for a total object. So, sinä becomes sinut.

Since the lesson is about accusative pronouns, when would I use sinut versus the partitive sinua?

You use the accusative sinut when an action is seen as complete or covers the "whole" object. An invitation to a place is a complete, single event, so we use sinut. You would use the partitive sinua for ongoing or incomplete actions, or for expressing feelings (like "I love you" — Rakastan sinua).

I thought "here" was täällä. Why does this sentence use tänne?

In Finnish, location words change depending on movement. täällä means being stationary "here" (for example, "I am here"). tänne means movement "(to) here". Because Mother is inviting you to come to this place, the action involves movement towards the speaker, so we must use the directional word tänne.

What is the dictionary form of kutsuu, and why does it end in a double u?