Пожалуйста, покажите ладонь: я хочу проверить, глубокая ли рана.

Покажите is the polite or plural imperative form of показать.

• покажи = show (to one person, informal)
• покажите = show (to one person politely, or to more than one person)

In a medical or professional situation, покажите is the natural choice.

Also, it comes from the perfective verb показать, which suggests a single completed action: show me your palm.

Russian often chooses between perfective and imperfective verbs.

• показать = perfective, to show once, to present
• показывать = imperfective, to be showing, to show repeatedly, to demonstrate in an ongoing way

Here the speaker wants one specific action: Please show me your palm. That is why показать / покажите is used.

In Russian, possessive words like вашу or свою are often omitted when the meaning is obvious from context.

So:

• Покажите ладонь = Show your palm
• Покажите вашу ладонь is possible, but usually less natural here

Since it is obvious that the person should show their own palm, Russian does not need to say it explicitly.

Because ладонь is an inanimate feminine noun of the third declension, and in the singular its accusative form is the same as its nominative form.

So:

• nominative: ладонь
• accusative: ладонь

It looks unchanged, but it is still functioning as the direct object of покажите.

No, they are not the same.

• ладонь = the palm of the hand
• рука = hand or arm, depending on context

So покажите ладонь specifically means show your palm, not just show your hand in a general sense.

Я хочу проверить means I want to check.

The infinitive проверить is perfective, which fits well because the speaker wants to perform one complete check and get a result.

Compare:

• я хочу проверить = I want to check
• я хочу проверять = I want to be checking / I want to check repeatedly

In this sentence, the one-time completed check is what matters.

Ли is used to form an indirect yes/no question, often translated as whether.

So:

• Я хочу проверить, глубокая ли рана. = I want to check whether the wound is deep.

A very literal breakdown is:

• глубокая = deep
• ли = whether
• рана = wound

The word before ли is usually the thing being focused on. Here the focus is on глубокая: whether the wound is deep.

Russian usually does not use a present-tense verb meaning is/am/are in sentences like this.

So:

• рана глубокая = the wound is deep
• literally, Russian just says something like wound deep

That is normal Russian grammar. The present-tense to be is usually omitted.

So in глубокая ли рана, the meaning is still whether the wound is deep, even though there is no separate word for is.

Because глубокая agrees with рана.

• рана is feminine
• singular
• nominative here

So the adjective must also be:

• feminine singular nominative → глубокая

This is standard adjective agreement in Russian.

Because глубокая ли рана is a subordinate clause attached to я хочу проверить.

Russian punctuation requires a comma before this kind of clause:

• Я хочу проверить, глубокая ли рана.

This is similar to English:

• I want to check whether the wound is deep.

The comma separates the main clause from the indirect question.

The colon introduces the explanation or reason for the request.

So the structure is:

• Please show your palm: I want to check whether the wound is deep.

The second part explains why the speaker is asking.

A dash could sometimes appear in similar contexts, but the colon works well here because the second clause clearly explains the first.