Tiski on täynnä astioita.

Here tiski most naturally means the sink in a kitchen context.

Depending on context, tiski can also mean a counter or desk of some kind, but in Tiski on täynnä astioita, the usual interpretation is The sink is full of dishes.

On is the 3rd person singular form of olla, which means to be.

So:

• tiski = sink
• on = is
• täynnä = full
• astioita = dishes

Literally, the structure is very close to English: Sink is full of dishes.

Täynnä means full, but it does not behave exactly like a basic adjective in this sentence.

In this pattern, täynnä is used in the expression:

täynnä + partitive = full of something

For example:

• Lasi on täynnä vettä. = The glass is full of water.
• Huone on täynnä ihmisiä. = The room is full of people.

So in Tiski on täynnä astioita, täynnä introduces what the sink is full of.

Because Finnish usually expresses that idea with täynnä + partitive case, not with a separate word meaning of.

So:

• English: full of dishes
• Finnish: täynnä astioita

The of idea is built into the construction.

Because after täynnä, Finnish normally uses the partitive.

So:

• astiat = the dishes / dishes as a nominative plural subject form
• astioita = dishes in the partitive plural

In this sentence, astioita is not the subject. It tells you what the sink is full of.

That is why Tiski on täynnä astioita is correct, while Tiski on täynnä astiat would be wrong.

The basic singular word is astia = dish, vessel, container.

Its plural forms are built from a plural stem:

• astia = dish
• astiat = dishes
• astioita = dishes (partitive plural)

This change is normal for many Finnish nouns of this type. The -oita ending here is a common plural partitive ending.

So astioita means something like some dishes / dishes in the grammatical form required by täynnä.

Finnish has no articles, so there is no separate word for the or a/an.

Whether tiski means a sink or the sink depends on context. In a normal household situation, English usually translates it as the sink.

So:

• Tiski on täynnä astioita
  usually = The sink is full of dishes

Yes, and the meaning is a little different.

• Tiski on täynnä astioita. = The sink is full of dishes.
• Tiskissä on astioita. = There are dishes in the sink.

The first sentence emphasizes fullness. The second just says that dishes are in the sink.

Also notice the form:

• tiski = sink
• tiskissä = in the sink

The ending -ssä means in.

Yes, Finnish word order is more flexible than English word order.

The neutral, ordinary order here is:

Tiski on täynnä astioita.

But other orders are possible for emphasis in the right context. Still, for a learner, this basic order is the safest and most natural.

So this sentence follows a very common pattern:

subject + on + täynnä + partitive noun

Because with a phrase naming the contents, täynnä is the normal form.

So Finnish says:

• Tiski on täynnä astioita.
• Lasi on täynnä vettä.

You can use täysi in some situations meaning full, but when you say what something is full of, täynnä + partitive is the standard pattern learners should remember.