Ellavu vian buŝon per buŝakvo.

Lavi means to wash.
Adding the prefix el- often gives the idea of out, outward, or thorough removal.

So:

• lavu = wash
• ellavu = wash out, rinse out

In this sentence, ellavu vian buŝon is the natural way to say rinse your mouth or wash out your mouth.

The ending -u is the Esperanto verb ending for a command, request, or instruction.

Examples:

• Manĝu! = Eat!
• Venu! = Come!
• Ellavu vian buŝon. = Rinse your mouth.

So ellavu is the imperative/jussive form of ellavi.

The -n marks the direct object.

In this sentence, the thing being rinsed is your mouth, so buŝo becomes buŝon.

• buŝo = mouth
• buŝon = mouth as the direct object

Esperanto uses -n very regularly for direct objects, even when English does not show any special ending.

Because via must agree with the noun it describes.

Since buŝon is:

• singular
• accusative (-n)

the possessive adjective also takes -n:

• via buŝo = your mouth
• vian buŝon = your mouth as the direct object

This is a very common Esperanto pattern: adjectives and similar words agree with the noun in number and case.

Per means by means of, using, or with in the sense of by using something as a tool or method.

So:

• per buŝakvo = with mouthwash / using mouthwash

This is different from English with, which can cover several meanings. In Esperanto, per specifically shows the means or instrument.

Examples:

• Mi skribas per krajono. = I write with a pencil.
• Li tranĉis ĝin per tranĉilo. = He cut it with a knife.

Buŝakvo is a compound word:

• buŝo = mouth
• akvo = water

So literally it means mouth-water, but the actual meaning is mouthwash.

Compounds like this are extremely common in Esperanto. Usually the final part is the main idea, and the earlier part modifies it:

• trinkakvo = drinking water
• manĝotablo = dining table / literally eating-table
• buŝakvo = mouthwash

Yes. Esperanto very often combines roots into a single word instead of using separate words.

That means learners will often see words that are easy to understand once broken apart. Here:

• buŝ-akv-o

This makes vocabulary efficient, because if you know the parts, you can often understand the whole word even if you have never seen it before.

Yes, it is understandable, but ellavu is more precise for rinse out.

• lavu = wash
• ellavu = wash out / rinse

If the intended meaning is specifically rinse your mouth, ellavu is the better choice.

Yes, Esperanto word order is fairly flexible because the grammar endings show what each word is doing.

For example, these are still understandable:

• Per buŝakvo ellavu vian buŝon.
• Vian buŝon ellavu per buŝakvo.

But Ellavu vian buŝon per buŝakvo is the most straightforward and neutral order.

The tricky letter for English speakers is ŝ.

• ŝ is pronounced like English sh
• so buŝo sounds roughly like BOO-sho
• buŝon sounds roughly like BOO-shon

A quick breakdown:

• bu = like boo
• ŝo = like sho
• -n = a clear final n

Esperanto spelling is very regular, so once you know the sound of ŝ, the word is easy to pronounce.

Not always, but it is very common and very clear.

Esperanto can sometimes omit the possessive when the owner is obvious from context, especially with body parts, but using vian here is completely natural and unambiguous.

So for a learner, vian buŝon is an excellent and safe choice for your mouth.