Peruste näkyy päätöksessä.

Näkyy is the 3rd person singular present tense of näkyä.

• näkyä = to be visible, to be seen, to appear
• näkyy = is visible / can be seen / appears

So the sentence is built around the idea that the basis/grounds are visible in the decision.

A useful contrast:

• näkyä = something is visible
• näyttää = something shows something, or looks like something

So this sentence is not saying that the basis shows the decision. It says the basis can be seen in the decision.

The ending -ssä is the inessive case, which usually means in.

So:

• päätös = decision
• päätöksessä = in the decision

This is why English uses in here, while Finnish uses a case ending instead of a separate preposition.

This is because päätös is an -s noun with a stem change.

Its forms go like this:

• nominative: päätös
• genitive: päätöksen
• inessive: päätöksessä

So the stem is päätökse- in most other forms.

Many Finnish nouns ending in -s behave like this:

• vastaus → vastauksen
• keskus → keskuksessa
• päätös → päätöksessä

This is something learners usually just have to get used to as a noun type.

Peruste is in the nominative singular.

Here it is the subject of the sentence:

• Peruste = the basis / the grounds / the justification
• näkyy = is visible / appears
• päätöksessä = in the decision

So literally the structure is:

Basis/grounds + is visible + in the decision

Not always. Peruste is one of those words whose best English translation depends on context.

Possible translations include:

• basis
• grounds
• justification
• reason

In legal or official language, grounds or justification are often very natural translations.

So even if the learner has already been shown the meaning, it is useful to know that peruste is a flexible word rather than a one-word match in every context.

Finnish normally has no articles, so there is no direct equivalent of the or a/an.

That means:

• peruste can mean a basis, the basis, or simply basis/grounds, depending on context
• päätöksessä can mean in a decision or in the decision

The surrounding context tells you which interpretation is intended.

No, it is not passive in Finnish.

Even though English often translates it as can be seen, Finnish is using a normal active verb:

• Peruste näkyy päätöksessä.
• literally: The basis is visible in the decision.

So näkyä naturally expresses the idea that something is visible, without needing a passive construction.

Yes. Finnish word order is fairly flexible, and changing it changes the focus or emphasis more than the basic meaning.

Neutral order:

• Peruste näkyy päätöksessä.

Other possible orders:

• Päätöksessä näkyy peruste.
  This puts more focus on in the decision.
• Näkyy peruste päätöksessä.
  This is much less neutral and would need a special context.

So the original sentence is a very natural, straightforward way to say it.

Because näkyä is an intransitive verb here.

It does not take a direct object in this kind of meaning. Instead, it works with:

• a subject: peruste
• possibly a place/location expression: päätöksessä

Compare:

• Peruste näkyy päätöksessä. = The grounds are visible in the decision.
• no object is needed

This is different from verbs that directly affect an object.

This is a very common source of confusion.

näkyä

means:

• to be visible
• to be seen
• to appear

Example:

• Peruste näkyy päätöksessä.
  The grounds are visible in the decision.

näyttää

can mean:

• to show
• to look / seem

Examples:

• Päätös näyttää perusteen.
  The decision shows the grounds.
• Se näyttää hyvältä.
  It looks good.

So in your sentence, näkyy is correct because the idea is that the grounds are visible, not that something shows them.

Not necessarily. Finnish often uses the inessive case -ssa / -ssä for both literal and more abstract in.

Here it is abstract:

• päätöksessä = in the decision

That means within the text/content of the decision, not physically inside an object.

This is completely normal in Finnish. The same case is used in many abstract expressions, for example:

• kirjassa = in the book
• sopimuksessa = in the agreement
• laissa = in the law

Yes, that is possible in a looser, more natural English style.

Because näkyä can mean:

• be visible
• appear
• show up

and because peruste can mean:

• basis
• grounds
• reason
• justification

the exact English wording can vary depending on context and style.

So all of these could be reasonable translations in the right context:

• The grounds are visible in the decision.
• The justification appears in the decision.
• The reason shows up in the decision.

The Finnish sentence itself is quite compact and leaves some of that choice to context.