Не могли бы Вы показать мне сандалии с мягким ремешком и туфли без каблуков?

This is a very common polite request pattern in Russian:

Не могли бы Вы + infinitive?

Literally, it looks like Couldn’t you... ?, but in real usage it means something more like:

Could you please... ?
or
Would you be able to... ?

The pieces are:

• не — part of the polite formula; it does not make the request truly negative
• могли — past tense plural of мочь (to be able)
• бы — particle that makes the meaning conditional, like would
• Вы — formal you

So Не могли бы Вы показать... ? is a soft, respectful way to ask someone to show something.

Вы is the formal or polite form of you in Russian. It is also the normal plural you.

In polite written Russian, people often capitalize it as Вы to show respect, especially in customer service, letters, or formal conversation. In many texts you may also see lowercase вы; both are possible, but the capital letter is extra polite.

Because formal Вы uses the same grammar as plural you, the verb is plural too:

• ты мог бы — informal singular
• Вы могли бы — formal singular or plural

So могли is plural because it agrees with Вы.

Russian often chooses between a perfective and an imperfective verb.

Here:

• показать = perfective
• показывать = imperfective

In this sentence, показать is used because the speaker is asking for one complete action: to show the items.

So Не могли бы Вы показать... means:

Could you show me... ?

If you used показывать, it would sound less natural here, because that form suggests an ongoing, repeated, or process-like action.

Because мне is the dative case form of я.

The verb показать often works like show someone something. The person receiving the showing is in the dative:

• показать мне — show me
• показать ему — show him
• показать нам — show us

So:

• я = I
• меня = me (often genitive or accusative)
• мне = to me / for me

Here the meaning is show to me, so Russian uses мне.

Because both nouns are plural here, and for inanimate plural nouns, the accusative usually looks the same as the nominative.

The speaker is asking to be shown:

• сандалии
• туфли

These are the direct objects of показать, so they are in the accusative. But since they are inanimate plural nouns, their accusative form is the same as the nominative form.

That is why you see:

• сандалии
• туфли

with no visible change.

Also, footwear is very often talked about in the plural, because it normally comes as a pair.

Because the preposition с here means with, and in this meaning it requires the instrumental case.

So:

• с ремешком = with a strap
• с мягким ремешком = with a soft strap

Both the noun and the adjective must go into the instrumental:

• мягкий → мягким
• ремешок → ремешком

This is normal Russian agreement: the adjective changes to match the noun in case, number, and gender.

Yes, in real life they often do. But Russian can still use the singular to describe a characteristic feature in a general way.

So с мягким ремешком can mean something like:

with a soft strap
or
with soft strapping in a general descriptive sense.

This does not necessarily mean there is literally only one strap. It is just a natural way to describe the style.

If the speaker wanted to emphasize multiple straps, they could say:

с мягкими ремешками

But the singular in the original sentence is perfectly normal.

Ремешок means a small strap or strap-like fastening, which fits footwear very well.

Compare:

• ремень — belt, strap; often something larger or more general
• ремешок — little strap, narrow strap

For sandals or shoes, ремешок sounds more natural because it refers to the kind of small strap you expect on footwear.

The ending -ок here gives a smaller, more specific sense.

Because the preposition без always takes the genitive case.

So:

• каблуки = heels
• after без, it becomes каблуков

That is why:

• без каблуков = without heels

This is a very important rule to remember:

• без + genitive

Examples:

• без сахара — without sugar
• без воды — without water
• без денег — without money

Because the sentence is talking about shoes as a pair, and a pair of shoes normally has heels in the plural.

So туфли без каблуков means:

shoes without heels

This is the most natural way to describe that type of footwear.

You may sometimes see singular forms in other contexts, but here the plural sounds very normal because the noun refers to the pair as a whole.

No, Russian word order is fairly flexible.

The given order is natural:

Не могли бы Вы показать мне сандалии с мягким ремешком и туфли без каблуков?

But some parts could move around without changing the basic meaning, for example:

Не могли бы Вы мне показать сандалии с мягким ремешком и туфли без каблуков?

The original version sounds neutral and smooth for a polite request in a shop.

Russian word order often changes for emphasis, rhythm, or style rather than basic grammar, because the case endings already show how the words relate to each other.