Learn Icelandic: Strákurinn mátar brúnan jakka og þykka peysu. - The boy tries on a brown jacket and a thick sweater.

Because it describes jakka (a jacket), which is a masculine noun. Since the jacket is the direct object being tried on, it is in the accusative case. Strong adjectives for masculine accusative nouns end in -an, turning the base word brúnn into brúnan.

If they are both masculine and accusative, why don't brúnan and jakka rhyme?

Nouns and adjectives follow different pattern rules. The base noun jakki is a weak masculine noun, and its accusative form ends in -a (jakka). Adjectives follow the strong pattern, which uses -an for the masculine accusative. Words must match in gender and case, but their actual endings will often look completely different!

Why does the adjective þykka (thick) end in -a instead of -an?

Because it describes peysu (a sweater), which is a feminine noun. Even though it is also in the accusative case like the jacket, feminine strong adjectives take an -a ending in the accusative. So the base word þykkur becomes þykka.

Is it the verb mátar that puts the clothes into the accusative case?