تحرك صديقتي قطعة اللعب من دون أن ترمي النرد.

Because Arabic very often uses verb–subject–object order.

So:

• تُحَرِّكُ صديقتي قطعة اللعب = My friend moves the game piece

This is completely normal in MSA. You could also say:

• صديقتي تُحَرِّكُ قطعة اللعب

That is also correct, but it gives a bit more emphasis to my friend.

Because Arabic usually writes without short vowels, تحرك can represent more than one fully vocalized form.

In this sentence, it is understood as:

• تُحَرِّكُ = she moves

That fits the subject صديقتي, which is feminine singular.

So the intended structure is:

• تُحَرِّكُ صديقتي...
• My friend moves...

It comes from حرّك in Form II, which means to move something or to make something move.

So:

• حرّك = moved something
• يحرّك / تُحرّك = moves / she moves

That is why this verb can take a direct object, here قطعة اللعب.

The base word is:

• صديقة = female friend

When you add the possessive suffix ـي meaning my, the ة becomes a pronounced ت:

• صديقة + ي → صديقتي

This is very common in Arabic:

• سيارة → سيارتي
• مدرسة → مدرستي
• صديقة → صديقتي

Literally, it means my female friend.

Depending on context, it can also mean my girlfriend, but in neutral MSA learning sentences it usually just means my female friend unless the context clearly suggests a romantic meaning.

Because this is an iḍāfa construction, which is a noun-to-noun structure often translated as X of Y.

So:

• قطعة اللعب = literally piece of play/game
• natural English: game piece or playing piece

In an iḍāfa:

• the first noun usually does not take ال
• the second noun can make the whole phrase definite

So قطعة اللعب is normal, while القطعة اللعب would not be the standard iḍāfa pattern.

In fully vocalized MSA, yes. You could write it as:

• تُحَرِّكُ صديقتي قطعةَ اللعبِ من دونِ أن ترميَ النردَ

But in normal Arabic writing, short vowels and case endings are usually omitted, so learners usually see:

• تحرك صديقتي قطعة اللعب من دون أن ترمي النرد

That is standard.

English often says:

• without + -ing
• without throwing

Arabic commonly expresses this idea with:

• من دون أن + present verb
• or بدون أن + present verb

So:

• من دون أن ترمي النرد = without throwing the die/dice

Literally, it is closer to without that she throw the die/dice, but the natural English translation is simply without throwing.

Yes. Both are used to mean without.

So these are both possible:

• من دون أن ترمي النرد
• بدون أن ترمي النرد

In MSA, من دون can sound a bit more formal or literary, but both are widely understood.

The verb is from:

• رمى = to throw

The present feminine singular form is:

• ترمي = she throws

After أن, the verb is in the subjunctive. With this kind of verb, the spelling usually looks the same in ordinary unvowelled text. In fully vocalized writing, you would see:

• ترميَ

So the grammar changes after أن, even if the normal spelling does not show much difference.

Because Arabic verbs already contain subject information.

The form ترمي already tells you the subject is feminine singular in this context, so Arabic does not need a separate word for she.

The subject is understood from the earlier noun:

• صديقتي

So the sentence means that my friend is the one who does both actions:

• she moves the piece
• she does not throw the die/dice

النرد refers to dice.

In game-related Arabic, يرمي النرد means to throw the die/dice, which is the usual Arabic expression. In English, we often say roll the dice, but Arabic commonly uses the verb throw here.

So:

• ترمي النرد = she throws / rolls the die or dice