Learn Finnish: Hän yrittää muistaa säännön toistamalla sitä. - He tries to remember the rule by repeating it.

This is the third infinitive adessive form of the verb toistaa (to repeat). You form it by taking the verb stem (toista-) and adding the suffix -malla (or -mällä, depending on vowel harmony). It is used to express how or by what means an action is achieved.

Why is "the rule" (säännön) in the genitive case, but "it" (sitä) in the partitive case?

Because they are the objects of two different verbs! Säännön is the object of muistaa (to remember). Successfully remembering something is viewed as a completed action, so it takes the total object case. On the other hand, sitä is the object of toistamalla (by repeating). Repeating is naturally an ongoing, continuous action, so toistaa requires its object to be in the partitive.

What happens to the word sääntö (rule) when it becomes säännön?

Adding the -n suffix closes the final syllable, which triggers consonant gradation. The strong -nt- combination in the middle of sääntö weakens to a double -nn-, resulting in säännön.

Why is muistaa in its basic dictionary form?