Learn Icelandic: Sólin er sterk fyrir húðina. - The sun is strong for the skin.

The preposition fyrir takes the accusative when it means 'for' in the sense of an intended purpose, benefit, or effect on something (like the sun's effect on the skin). It typically takes the dative when referring to physical location ('in front of') or time ('ago').

Why is the adjective sterk and not sterkur?

Adjectives must agree in gender, number, and case with the noun they describe. Because sólin (the sun) is a feminine singular noun in the nominative case, the adjective drops the masculine -ur ending and becomes the feminine sterk.

How does the word for skin, húðina, get its ending?

The base word is húð (skin), which is a feminine noun. Because it follows fyrir, it must be in the accusative case. The attached definite article ('the') for a feminine singular accusative noun is -ina, which combines with the base to make húðina.

If I wanted to say 'for my skin' or 'for your skin', would I add a possessive pronoun here?

You can, but it is often unnecessary in Icelandic. When talking about body parts, Icelandic frequently relies on just the definite article (like húðina) to mean 'your skin' or 'one's skin', whereas English would naturally use a possessive word.