Learn Icelandic: Hesturinn stekkur yfir girðinguna.

The preposition yfir (over) takes the accusative case when it describes active movement or a change in location. Because the horse is actively jumping across the fence, we use the accusative. If something were just resting stationary above the fence, yfir would take the dative case instead.

What is the base word for girðinguna and how is its ending formed?

The base word is the feminine noun girðing (fence). In the accusative case, this base noun doesn't change its spelling, but we need to add the definite article (the attached ending for "the"). For feminine nouns in the accusative, that ending is -una, giving us girðinguna.

The infinitive verb is stökkva (to jump). Why does it look like stekkur here?

Stökkva is a strong verb, which means it changes its inner vowel when conjugated instead of just taking a standard ending. In the present tense for singular subjects like hesturinn (the horse), the ö changes to an e, making it stekkur.

Why is the subject written as hesturinn instead of just hestur?

Hestur simply means "a horse". To say "the horse", Icelandic attaches the definite article to the end of the word. Since hestur is a masculine noun in the nominative case (because the horse is the one doing the jumping), it takes the -inn ending to become hesturinn.