Learn Icelandic: Skoðun þeirra beggja er mjög svipuð. - The opinion of both of them is very similar.

beggja is the genitive (possessive) form of báðir (both). To express 'of both of them', Icelandic groups the genitive of 'they' (þeirra) with the genitive of 'both' (beggja), which literally translates to 'of them of both'.

Why doesn't skoðun have the definite article attached (skoðunin) since the English translation says 'The opinion'?

In Icelandic, when a noun is followed by a possessive pronoun like þeirra, it typically drops the definite article suffix. You just use the base noun skoðun alongside the possessive.

Why does þeirra beggja come after Skoðun instead of before it?

Unlike English, which puts possessives before the noun ('their opinion'), Icelandic usually places possessive pronouns and phrases directly after the noun they belong to.

Why does the adjective svipuð end in -uð here?

The adjective must match the noun it describes in gender, number, and case. Because skoðun is a feminine, singular noun in the nominative case, the root adjective svipaður (similar) changes to its feminine singular nominative form, which is svipuð.