Breakdown of Ég veit að traustið á milli ykkar beggja er mikið.
vera
to be
ég
I
vita
to know (a fact, information)
að
that (conjunction)
Questions & Answers about Ég veit að traustið á milli ykkar beggja er mikið.
Why do we use beggja here instead of báðir or báðum?
The preposition á milli (between) always requires the genitive case. Because of this, the pronoun þið (you plural) becomes ykkar, and the word for "both" must agree with its case, taking the genitive form beggja.
In English we say "both of you," but the Icelandic says ykkar beggja. Why is the order reversed?
In Icelandic, you don't use a structure like "both of [pronoun]." Instead, the personal pronoun comes first, followed directly by the word for "both" in the matching case. So, "both of you" is literally phrased as "you both": ykkar beggja.
Could I just say milli ykkar beggja without the word á?
Yes, you can. Both á milli and milli mean "between" and both force the following nouns or pronouns into the genitive case. Á milli is just a very common set phrase, especially when talking about relationships or distance between people.
Why does the sentence end with the neuter form mikið?
The adjective mikið (great/much) is describing the subject of the clause: traustið (the trust). Because traust is a neuter noun, the adjective has to match it by taking the neuter singular nominative form.