Utrumque mihi placet.

Utrumque is from uterque, utraque, utrumque, which means each of the two or, more naturally in English, both.

In this sentence it stands on its own, without a noun, so it means both things or both of them.

Because uterque is grammatically singular in Latin, even though its meaning involves two items.

Its basic idea is not just both together, but each one of the two. So Latin often uses singular grammar where English would naturally use a plural translation.

That is why utrumque can be translated as both, even though its form is singular.

Here it is nominative neuter singular.

The form utrumque could be either nominative or accusative neuter singular in isolation, but in this sentence it must be nominative because it is the subject of placet.

Latin is literally saying something like both things are pleasing to me.

Because the verb placere works differently from English to like.

In English, we say I like it.
In Latin, the construction is more like it is pleasing to me.

So:

• that which is liked = subject
• the person who likes it = dative

That is why Latin uses mihi (to me) rather than ego (I).

Because its subject, utrumque, is grammatically singular.

Even though English translates the idea as both, Latin treats uterque / utraque / utrumque as singular in form, so the verb is singular too:

• utrumque ... placet = both please me / I like both

If Latin used a truly plural word such as ambo, then the verb would normally be plural:

• ambo mihi placent

Historically, yes: it is the same enclitic -que.

But in this word, you should treat utrumque as a single fixed form meaning each of the two / both. You do not translate it as if it were uter + and in the sentence.

So here utrumque simply means both or each of the two.

Because it refers to things, not specifically masculine or feminine persons or nouns.

The forms are:

• uterque = masculine
• utraque = feminine
• utrumque = neuter

So utrumque mihi placet suggests both things rather than both men or both women.

Yes. Latin word order is flexible.

The sentence could also appear as:

• Mihi utrumque placet
• Utrumque placet mihi
• Placet mihi utrumque

The basic meaning stays the same. Word order mainly affects emphasis:

• utrumque first: emphasis on both
• mihi first: emphasis on to me
• placet early: emphasis on the idea of pleasing

The given order, Utrumque mihi placet, is perfectly natural.

That is a very useful comparison.

• utrumque mihi placet = literally each of the two pleases me
• ambo mihi placent = both please me

The difference is:

• uterque / utraque / utrumque is grammatically singular and often has a slightly distributive sense: each of the two
• ambo / ambae / ambo is grammatically plural and means both together

In many contexts, both can be translated naturally as I like both, but the grammar is different.