Ergonomický pracovní kout je pohodlný.

Because they are all in the masculine singular nominative form.

The noun kout is masculine singular, so any adjective describing it must agree with it in:

• gender
• number
• case

Here:

• ergonomický = ergonomic
• pracovní = work / working
• pohodlný = comfortable

All three are matching kout.

Kout is a masculine inanimate noun.

A useful beginner rule is:

• nouns ending in a consonant are often masculine

That rule is not perfect, but it works here.

So:

• ten kout = that corner / nook

Because it is masculine, the adjectives take masculine forms:

• ergonomický kout
• pohodlný kout

Pracovní kout is a noun phrase meaning something like:

• work corner
• work nook
• workspace area

Literally:

• pracovní = work-related
• kout = corner, nook

In context, it suggests a small area set up for work, like a desk corner or compact workspace.

Je is the 3rd person singular present form of být = to be.

So:

• je = is

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

• Ergonomický pracovní kout = the subject
• je pohodlný = is comfortable

Unlike in some other Slavic languages, in standard Czech you normally do use the present form je in sentences like this.

Because with a sentence like this, the adjective after být normally agrees with the subject and appears in the nominative.

So:

• kout = nominative
• pohodlný = nominative masculine singular to match it

This is very common in Czech:

• Dům je velký. = The house is big.
• Stůl je nový. = The table is new.

Because Czech does not have articles.

English requires:

• a comfortable workspace
• the comfortable workspace

Czech usually leaves that idea to context:

• Ergonomický pracovní kout je pohodlný.

Depending on context, it could mean:

• An ergonomic workspace is comfortable
• The ergonomic workspace is comfortable

Context tells you which one is meant.

A rough pronunciation guide is:

er-go-NO-mits-kee PRA-tsov-nee kout ye po-HODL-nee

A few helpful notes:

• Stress in Czech is usually on the first syllable of each word.
• ý is a long vowel.
• ou in kout is a diphthong, roughly like oh-oo blended together.
• je sounds like ye.

A more IPA-like version is:

[ˈɛrɡonomɪtskiː ˈpratsovniː kout jɛ poˈɦodlniː]

Yes, Czech word order is fairly flexible, but the original sentence is the most neutral and natural order.

Neutral:

• Ergonomický pracovní kout je pohodlný.

If you change the order, you usually change the emphasis:

• Pohodlný je ergonomický pracovní kout.
  This sounds marked and emphasizes comfortable.

So for a basic statement, the original order is the best choice.

Usually here, yes: comfortable.

But pohodlný can sometimes have slightly broader meanings depending on context, such as:

• comfortable
• convenient
• easy / relaxed

In this sentence, with pracovní kout, the natural meaning is comfortable or pleasant to use.

You replace je with není:

• Ergonomický pracovní kout není pohodlný.
• The ergonomic workspace is not comfortable.

This is the normal way to negate to be in the present tense.

A simple yes/no question is:

• Je ergonomický pracovní kout pohodlný?
• Is the ergonomic workspace comfortable?

Czech often forms yes/no questions mainly through intonation or by putting the verb first, as here.

Then the adjectives and verb would change to agree with the plural noun.

Singular:

• Ergonomický pracovní kout je pohodlný.

Plural:

• Ergonomické pracovní kouty jsou pohodlné.

Changes:

• kout → kouty
• je → jsou
• ergonomický → ergonomické
• pohodlný → pohodlné

This is a good example of how important agreement is in Czech.