Learn Russian: Мы берём эту коричневую сумку, потому что магазин даёт скидку. - We are taking this brown bag, because the shop is offering a discount.

This phrase is the direct object of the verb берём (we are taking), meaning it is the thing being taken. Therefore, it must be in the accusative case. The feminine noun сумка changes its -а ending to -у (сумку). To match it, the demonstrative pronoun эта (this) changes to эту, and the adjective коричневая (brown) changes its -ая ending to -ую (коричневую).

I know the verb for "to take" is брать. Why does it look like берём here?

Берём is the "we" form of брать. This is an irregular verb that changes its stem in the present tense. Instead of keeping the -а- from the infinitive, the present tense forms use -е- or -ё-: я беру, ты берёшь, он/она берёт, мы берём, вы берёте, они берут.

Why do we use даёт for "is offering"? Doesn't давать mean "to give"?

Yes, it literally means the shop "gives" a discount. In Russian, the standard way to say a shop is offering a discount or having a sale is давать скидку (to give a discount). Also notice the conjugation: the verb давать drops the -ва- in the present tense, making it даёт, not "давает".

Why does the sentence end with instead of ?