Ten styl jest nowy.

Because styl is a masculine singular noun, and the demonstrative ten has to agree with it in gender, number, and case.

In the nominative singular:

• ten = masculine
• ta = feminine
• to = neuter

So:

• ten styl = this style
• not ta styl
• not to styl

In Polish, nouns that end in a consonant are often masculine, and styl ends in -l.

So styl is:

• singular
• masculine
• here, in the nominative case

That is why both words around it also use masculine forms:

• ten
• nowy

Adjectives in Polish must agree with the noun they describe.

Since styl is:

• masculine
• singular
• nominative

the adjective must also be:

• masculine
• singular
• nominative

So we get:

• nowy for masculine
• nowa for feminine
• nowe for neuter

Compare:

• Ten styl jest nowy.
• Ta książka jest nowa.
• To krzesło jest nowe.

It is in the nominative case.

That is because styl is the subject of the sentence:

• Ten styl = the thing being talked about
• jest nowy = what is being said about it

Since ten styl is nominative, the agreeing words are nominative too:

• ten
• styl
• nowy

Jest is the 3rd person singular present tense of być = to be.

So:

• jest = is

In this sentence, it links the subject and the description:

• Ten styl = this style
• jest nowy = is new

So the structure is very similar to English:

• This style is new.

In standard Polish, you normally do use jest in a sentence like this.

Usually not in a sentence like this.

Polish sometimes drops forms of to be in very informal, special, or headline-like language, but in normal standard speech and writing you should say:

• Ten styl jest nowy.

not simply:

• Ten styl nowy.

So for learners, it is safest to keep jest here.

The neutral, most natural order is:

• Ten styl jest nowy.

Polish word order is more flexible than English, so other orders are possible, but they usually change the focus or emphasis.

For example:

• Nowy jest ten styl. = emphasizes new
• Ten nowy styl... = means this new style..., where nowy directly describes the noun inside the noun phrase

So if you just want a simple neutral sentence, use:

• Ten styl jest nowy.

That is a very common confusion.

Here, ten is a demonstrative adjective modifying a masculine noun:

• ten styl = this style

But to can be:

1. the neuter form of the demonstrative adjective
   
   • to okno = this window
2. a pronoun meaning something like this / it / that
   • To jest nowe. = This/It is new.

So in your sentence, because styl is masculine, you need:

• ten styl

not:

• to styl

A simple approximate pronunciation is:

• ten ≈ ten
• styl ≈ stil
• jest ≈ yest
• nowy ≈ NO-vih

A few helpful notes:

• y in Polish is not the same as English y. It is a separate vowel, somewhat like a short, central i sound.
• j is pronounced like English y in yes
• w is pronounced like English v

So nowy sounds roughly like NO-vih, not like English now-ee.

Yes. Styl is a broad word and can refer to different kinds of style depending on context, for example:

• artistic style
• writing style
• fashion style
• manner or mode

So the sentence Ten styl jest nowy could mean different things depending on the situation, but grammatically it works the same way.

The demonstrative, adjective, and sometimes the verb form must change to match.

Examples:

• Ten styl jest nowy. = This style is new.
  masculine singular

• Ta moda jest nowa. = This fashion is new.
  feminine singular

• To krzesło jest nowe. = This chair is new.
  neuter singular

• Te style są nowe. = These styles are new.
  plural

Notice:

• ten / ta / to / te
• nowy / nowa / nowe
• jest becomes są in the plural

Yes, but it means something slightly different in structure.

• Ten styl jest nowy. = This style is new.
  You start with this style as the subject.

• To jest nowy styl. = This is a new style.
  You start with this/it and then identify it.

Both are correct, but they are not exactly the same sentence pattern.

Polish does not have articles like English a and the.

So Polish uses context, word order, and words like demonstratives to express that meaning.

Here:

• ten already gives the idea of this
• so no article is needed

That is normal in Polish.