Learn Russian: Она не помнит этот текст.

The verb is помнит (remembers), which comes from the infinitive помнить (to remember). Because it ends in -ить, it belongs to the second conjugation. For the she (она) form, we drop -ить and add -ит. First conjugation verbs, on the other hand, usually take -ет.

Is the accusative case being used for этот текст?

Yes, этот текст is the direct object here (the thing being remembered), so it must be in the accusative case. Because текст is a masculine inanimate noun (not a living being), its accusative form looks exactly the same as its dictionary form. The word этот (this) matches that rule as well.

Where is the stress in the word помнит?

The stress is on the first syllable, the о. Because the ending -ит is unstressed, you will hear a clear and longer o sound at the beginning, while the ending is spoken more quickly and softly.

Why is не placed exactly there?

In Russian, the negative word не (not) almost always goes directly in front of the verb it is negating. Here, it sits right before помнит to mean does not remember.