Mogę przesuwać pionek.

Mogę is the 1st person singular form of móc, which means can / be able to.

So:

• mogę = I can
• możesz = you can
• może = he/she/it can

In this sentence, Mogę przesuwać pionek means I can move a pawn or I am able to move a pawn.

After móc (to be able to / can), Polish normally uses another verb in the infinitive.

So the structure is:

• mogę + infinitive

Examples:

• Mogę iść = I can go
• Mogę mówić = I can speak
• Mogę przesuwać = I can move / I can be moving

That is why you do not say a conjugated form after mogę here.

This is about aspect, which is very important in Polish.

• przesuwać = imperfective
• przesunąć = perfective

Very roughly:

• imperfective focuses on the action as ongoing, repeated, general, or simply possible
• perfective focuses on a completed action, often a single result

So:

• Mogę przesuwać pionek suggests I can move a pawn / I’m allowed or able to move the pawn, with no special focus on completing one move as a finished event.
• Mogę przesunąć pionek would sound more like I can move the pawn once / I can make that move successfully.

In many learning contexts, the imperfective is used for a general ability or permission.

Pionek here is the direct object, so it is in the accusative case.

For many masculine inanimate nouns, the accusative singular looks the same as the nominative singular. That is what happens here.

So:

• nominative: pionek
• accusative: pionek

Even though the form does not change, the grammatical role does: in this sentence it is the thing being moved.

Pionek usually means pawn, especially in chess or board-game contexts.

It can also mean a small playing piece more generally, depending on context.

So in a game setting, Mogę przesuwać pionek most naturally means I can move a pawn or I can move the playing piece.

Not usually by itself.

Mogę przesuwać pionek most naturally means:

• I can move a pawn
• I am able to move a pawn
• I’m allowed to move a pawn

If you want to ask May I move a pawn?, Polish would normally use question intonation or a clearer question form, for example:

• Czy mogę przesunąć pionek? = May I move the pawn? / Can I move the pawn?

So the sentence you were given is a statement, not a question.

Because Polish does not need a separate word like English to in this structure.

English says:

• I can move

Polish says:

• Mogę przesuwać

The second verb appears in the infinitive, and that already carries the meaning that English often expresses with to in other structures.

For example:

• Chcę iść = I want to go
• Muszę pracować = I have to work
• Mogę przesuwać = I can move

Yes, Polish word order is more flexible than English, although the neutral order here is very natural:

• Mogę przesuwać pionek.

You might also see:

• Pionek mogę przesuwać.
• Mogę pionek przesuwać.

These alternatives can add emphasis or sound more context-driven. For example:

• Pionek mogę przesuwać, ale wieży nie.
  = I can move the pawn, but not the rook.

For a learner, the original order is the best basic pattern to remember.

A rough pronunciation is:

• mogę ≈ MOH-gheh, with the final vowel nasalized

A bit more carefully:

• mo- as in more without the r
• g
• ę is a nasal vowel, often sounding a bit like eh with nasal coloring, and at the end of a word in normal speech it may sound less strongly nasal than learners expect

So learners often pronounce it approximately as MOH-gheh, which is a reasonable start.

It can look intimidating, but it becomes easier if you split it up:

• prze-su-wać

A rough guide:

• prze ≈ psheh
• su ≈ soo
• wać ≈ vach or vahtch, depending on how detailed your approximation is

The rz in prze- sounds like the Polish ż, similar to the s in measure or the zh sound in vision, though not exactly identical.

The final -ać is a very common infinitive ending in Polish verbs.

It can be either, depending on context.

Mogę can mean:

• I can in the sense of I am able
• I can in the sense of I am allowed

So Mogę przesuwać pionek could mean:

• I am physically or practically able to move the pawn
• The rules allow me to move the pawn

Context tells you which meaning is intended.

Often, if someone is talking about making one specific move, Polish may prefer the perfective:

• Mogę przesunąć pionek.

That sounds like I can move the pawn as a single completed move.

But if the idea is more general, habitual, or about what the rules permit in principle, przesuwać works well:

• Mogę przesuwać pionek = I can move a pawn / I’m allowed to move the pawn

So both are possible, but they highlight slightly different things.

No. Polish usually drops subject pronouns when they are not needed.

So:

• Mogę przesuwać pionek already means I can move a pawn

You could say:

• Ja mogę przesuwać pionek

but that adds emphasis, something like:

• I can move the pawn

In normal neutral speech, leaving out ja is more natural.