Na dużej tablicy wiszą dwadzieścia liter z kolorowego papieru.

Because after na meaning on in a static location, Polish uses the locative case.

So:

• tablica = nominative, basic dictionary form
• na tablicy = on the board, locative

The adjective has to match the noun, so:

• duża tablica = a big board
• na dużej tablicy = on a big board

Both words change because Polish adjectives agree with the noun in case, gender, and number.

Because this sentence describes location, not movement.

• na dużej tablicy = on the big board → location, so locative
• na dużą tablicę = onto the big board → movement toward a surface, so accusative

A useful contrast:

• Litery wiszą na dużej tablicy. = The letters are hanging on the big board.
• Wieszam litery na dużą tablicę. = I am hanging the letters onto the big board.

So the key question is: Where? or Where to?

Because Polish often prefers a specific verb that describes how something is positioned.

• wiszą = are hanging
• są = are

In English, you might say There are twenty letters on the board, but in Polish it is very natural to say what the letters are physically doing:

• wiszą = they are hanging
• leżą = they are lying
• stoją = they are standing

So Na dużej tablicy wiszą... sounds vivid and natural.

You may also hear sentences with jest / są, but wiszą is more descriptive here.

Because numbers 5 and above normally require the noun in the genitive plural.

So with litera:

• jedna litera = one letter
• dwie / trzy / cztery litery = two / three / four letters
• pięć / dziesięć / dwadzieścia liter = five / ten / twenty letters

That is why the sentence has:

• dwadzieścia liter

not dwadzieścia litery.

This is one of the most important number patterns in Polish.

This is a very good question, because numeral agreement in Polish can be tricky.

With numerals like pięć, dziesięć, dwadzieścia, learners often see sentences where the verb is singular, especially in more formal or traditional grammar:

• Na tablicy wisi dwadzieścia liter.

But in real usage, many speakers also use plural agreement, especially when they think of the items as a visible group of separate objects:

• Na tablicy wiszą dwadzieścia liter.

So this sentence uses the plural form wiszą, treating the letters as an ordinary plural set. A learner should know that this area has some variation, and both patterns may be encountered.

Here z means made of / out of, and in that meaning it normally takes the genitive.

So:

• papier = paper
• papieru = of paper

The adjective changes to match:

• kolorowy papier = colored paper
• z kolorowego papieru = out of colored paper

This is different from z meaning with, which uses the instrumental:

• z kolegą = with a friend

So here it is not with colored paper. It is made from colored paper.

Literally, it describes the paper.

• litery z kolorowego papieru = letters made of colored paper

So the structure is:

• litery = letters
• z papieru = made of paper
• z kolorowego papieru = made of colored paper

If you wanted to say colorful letters, you would more directly say:

• kolorowe litery

In this sentence, the letters may of course be colorful in appearance, but grammatically the adjective belongs to papieru.

Yes, Polish word order is fairly flexible.

This order is natural because it starts with the place and then tells you what is there:

• Na dużej tablicy = setting the scene
• wiszą = what is happening there
• dwadzieścia liter = what you can see

Other orders are possible, for example:

• Dwadzieścia liter wiszą na dużej tablicy.
• Z kolorowego papieru wiszą na dużej tablicy dwadzieścia liter. — possible, but less natural

The original sentence sounds like a normal description of a scene: On the big board, twenty letters are hanging.

Here are the main forms:

• na = on
• duży = big
• tablica = board
• wisieć = to hang
• dwadzieścia = twenty
• litera = letter
• z = from / made of
• kolorowy = colored / colorful
• papier = paper

And here is how they appear in the sentence:

• duży → dużej
• tablica → tablicy
• wisieć → wiszą
• litera → liter
• kolorowy → kolorowego
• papier → papieru

Seeing both the dictionary form and the sentence form is very useful in Polish, because endings change a lot.