De muilkorf ligt naast de bench.

Dutch often uses a position verb to describe where something is. For objects, the most common ones are:

• liggen = to lie
• staan = to stand
• zitten = to be located/stuck/contained in some way

A muilkorf is being thought of as an object that is lying somewhere, so Dutch uses ligt.

So Dutch prefers:

• De muilkorf ligt naast de bench.

rather than simply:

• De muilkorf is naast de bench.

That second version is not the normal choice for physical location.

This is a very common question for English speakers, because English often just uses is.

A simple rule:

• use liggen for things seen as lying flat, resting, or having no upright position
• use staan for things seen as upright or standing on a base

Examples:

• Het boek ligt op tafel.
  The book is lying on the table.
• De fles staat op tafel.
  The bottle is standing on the table.

In your sentence, a muilkorf is naturally thought of as lying somewhere, so ligt is the normal verb.

Because both nouns take the common-gender article de.

In Dutch, singular nouns usually take either:

• de
• het

Unfortunately, this often has to be learned word by word. There is not always a reliable rule.

So you simply learn:

• de muilkorf
• de bench

And in the plural, both would also take de:

• de muilkorven
• de benches

In Dutch, bench often means a dog crate or dog cage, especially in pet-related contexts.

This can confuse English speakers, because English bench usually means a seat or long chair. In Dutch, that meaning exists too in some contexts, but when talking about dogs, bench very often means a crate.

So in this sentence, de bench is most likely a dog crate.

Yes. Dutch uses many loanwords from English, and bench is one of them.

Even though it comes from English, it behaves like a normal Dutch noun:

• it takes an article: de bench
• it can be pluralized: benches
• it fits into normal Dutch sentence structure

Loanwords are very common in modern Dutch.

Naast means next to or beside.

It introduces a phrase showing location:

• naast de bench = next to the crate

So the sentence structure is:

• De muilkorf = subject
• ligt = verb
• naast de bench = place/location phrase

It works very much like English next to the crate, although Dutch uses naast as a single word.

This is the normal Dutch word order for a main clause:

• subject
• finite verb
• the rest of the sentence

So:

• De muilkorf = subject
• ligt = finite verb
• naast de bench = adverbial phrase of place

This is a standard Dutch pattern.

If you move the location phrase to the front, the verb must still stay in second position:

• Naast de bench ligt de muilkorf.

That is also correct.

Not as the normal way to describe location.

Dutch strongly prefers the position verb here, so you would say:

• Naast de bench ligt de muilkorf.

Using is instead of ligt sounds unnatural in this context.

A rough guide for English speakers:

• muil sounds a bit like mowl or myle, but with the Dutch ui sound, which is difficult and does not match English exactly
• korf sounds roughly like korf, with a short o

So approximately:

• MUIL-korf

The stress is on the first syllable: MUIL.

Also, ui is one of the harder Dutch vowel sounds for English speakers, so it is normal if it takes practice.

Yes. Dutch very often combines nouns into one word.

Here:

• muil = muzzle / snout / mouth area
• korf = basket

Together:

• muilkorf = muzzle

This is very typical Dutch word formation. English often uses separate words where Dutch uses one compound word.

The usual plurals are:

• muilkorven
• benches

Examples:

• De muilkorven liggen in de kast.
• De benches staan in de garage.

Notice that in the plural, Dutch uses de for both:

• de muilkorven
• de benches

In normal usage, muilkorf usually refers to an animal muzzle, especially a dog muzzle.

So in a sentence with bench, the pet context is especially strong:

• a dog muzzle
• next to a dog crate

A learner would normally interpret it that way unless the wider context suggests something unusual.