Das Putzmittel steht im Schrank neben dem Spülmittel.

Das is the neuter definite article, meaning the.

So:

• das Putzmittel = the cleaning product / the cleaner

German nouns have grammatical gender, and Putzmittel is neuter, so it takes das in the nominative singular.

Putzmittel is a common German noun for a cleaning product, cleaner, or cleaning agent.

It is made from:

• putzen = to clean
• Mittel = means, substance, product, agent

So literally it is something like cleaning agent.

German often uses specific position verbs where English might simply use is.

• stehen = to stand
• liegen = to lie
• sitzen = to sit

In this sentence, steht is used because the cleaning product is understood as being in an upright position.

So German prefers:

• Das Putzmittel steht im Schrank.
  = The cleaner is in the cupboard.

Even though English just says is, German often chooses a verb that describes how the object is positioned.

Im is a contraction of:

• in dem → im

So:

• im Schrank = in the cupboard / in the cabinet

This contraction is extremely common in German.

Because this sentence describes location, not movement.

German uses in with two different cases:

• dative for location: where?
• accusative for direction/movement: where to?

Here the cleaner is already inside the cupboard, so it is a location:

• im Schrank = in the cupboard
  (dative)

If you were talking about putting it into the cupboard, you would use the accusative:

• Ich stelle das Putzmittel in den Schrank.
  = I put the cleaner into the cupboard.

Because in is a two-way preposition and here it takes the dative case to show location.

The noun Schrank is masculine:

• nominative: der Schrank
• dative: dem Schrank

So:

• in dem Schrank
• contracted: im Schrank

Because neben here also describes location, so it uses the dative.

The phrase means the cleaner is located next to the dishwashing liquid.

Spülmittel is neuter:

• nominative: das Spülmittel
• dative: dem Spülmittel

So:

• neben dem Spülmittel = next to the dishwashing liquid

If there were movement toward a position next to it, then you could get the accusative in another sentence, for example:

• Ich stelle das Putzmittel neben das Spülmittel.
  = I place the cleaner next to the dishwashing liquid.

Spülmittel usually means dishwashing liquid or dish soap.

It comes from:

• spülen = to rinse / wash dishes
• Mittel = product / agent

So literally it is something like washing/rinsing agent.

Because in German, all nouns are capitalized.

That is why you see:

• Putzmittel
• Schrank
• Spülmittel

This is one of the most noticeable spelling rules in German.

The basic structure is:

• Das Putzmittel = subject
• steht = verb
• im Schrank = location
• neben dem Spülmittel = more specific location

So the sentence follows the normal German main-clause pattern:

Subject + verb + other information

German main clauses usually place the finite verb in second position, and that is exactly what happens here:

• Das Putzmittel | steht | im Schrank neben dem Spülmittel

Yes, that is grammatically correct, and a German speaker would understand it.

However, steht sounds more natural if the item is imagined as upright, like a bottle standing in a cupboard.

So:

• ist = more general
• steht = more specific and often more idiomatic in this context

German often prefers the more specific position verb.

It describes the location of the cleaning product.

The full idea is:

• the cleaner is in the cupboard
• and within that cupboard, it is next to the dishwashing liquid

So im Schrank gives the general location, and neben dem Spülmittel gives a more precise one.

You can think of the sentence as:

• The cleaner is standing [in the cupboard] [next to the dish soap].

A natural English translation would be:

• The cleaner is in the cupboard next to the dishwashing liquid.

A more literal version would be:

• The cleaning product is standing in the cupboard next to the dishwashing liquid.

But in normal English, we usually just say is, not is standing, unless the position really matters.