गीले कपड़े निचोड़कर बाहर सुखाइए।

Because कपड़े is masculine plural, and the adjective has to agree with it.

• गीला कपड़ा = wet cloth / wet garment
• गीले कपड़े = wet clothes

So:

• गीला = masculine singular
• गीले = masculine plural

Here कपड़े means clothes, so गीले is the correct matching form.

कपड़े literally comes from कपड़ा, which means cloth or a piece of clothing. In the plural, कपड़े very commonly means clothes.

So in this sentence, गीले कपड़े is best understood as:

• wet clothes

not just wet cloth in a general material sense.

निचोड़कर means after wringing, having wrung out, or by wringing out.

It is built from:

• निचोड़ना = to squeeze / wring out
• -कर = a connector meaning something like having done X, then...

So:

• निचोड़कर = after wringing out

In the sentence, it shows the first action happens before the second one:

1. wring out the wet clothes
2. dry them outside

Not exactly. It is often closer to:

• having done...
• after doing...
• sometimes by doing...

So निचोड़कर बाहर सुखाइए does not simply mean wring and dry in a loose English sense. It more specifically suggests sequence:

• Wring them out, then dry them outside.

This -कर form is very common in Hindi for linking actions.

Examples:

• खाना खाकर सो जाइए। = Eat and then go to sleep.
• दरवाज़ा खोलकर अंदर आइए। = Open the door and come inside.

Because सूखना and सुखाना are different:

• सूखना = to dry / to become dry
  
  • intransitive
  • the thing dries by itself
• सुखाना = to dry something
  
  • transitive
  • someone causes the thing to dry

In this sentence, the speaker is telling someone to do something to the clothes, so Hindi uses the transitive verb:

• सुखाइए = please dry them

Compare:

• कपड़े सूख रहे हैं। = The clothes are drying.
• कपड़े सुखाइए। = Dry the clothes.

सुखाइए is a polite imperative form.

It is used when telling someone respectfully to do something:

• सुखाओ = informal command
• सुखाइए = polite/respectful command

So this sentence sounds like:

• Please dry the wet clothes outside after wringing them out.

This form is commonly used for:

• respectful speech
• instructions
• requests
• household directions
• signs or formal guidance

It is a polite command/instruction.

Hindi often uses polite imperative forms in places where English might use either:

• Please dry...
• Dry...
• You should dry...

So depending on context, it could sound like:

• a respectful request to one person
• an instruction in a household setting
• a polite direction on a label or in a guide

The -इए ending makes it respectful rather than blunt.

Because बाहर here functions as an adverb, meaning outside.

So:

• बाहर सुखाइए = dry [them] outside

You do not need a postposition here.

Compare:

• बाहर जाइए। = Go outside.
• बाहर रखिए। = Keep it outside.

Sometimes Hindi also uses बाहर in combinations like:

• घर के बाहर = outside the house

But in this sentence, plain बाहर is enough.

It is understood from context. Hindi often leaves out objects once they are already clear.

Here:

• गीले कपड़े = the wet clothes
• सुखाइए = dry [them]

So English needs them, but Hindi does not have to repeat it.

A more literal breakdown would be something like:

• Wet clothes, wringing-out, outside dry-please

Natural English then becomes:

• Wring out the wet clothes and dry them outside.

The structure is:

• गीले कपड़े = object phrase
• निचोड़कर = after wringing out
• बाहर = outside
• सुखाइए = dry (polite imperative)

So the order is roughly:

• [wet clothes] [after wringing out] [outside] [dry]

Hindi often puts the main verb at the end. English usually rearranges this into something more natural, such as:

• Wring out the wet clothes and dry them outside.
• After wringing out the wet clothes, dry them outside.

Yes, in everyday speech many speakers say निचोड़ के instead of निचोड़कर.

• निचोड़कर = more standard/written/full form
• निचोड़ के = very common in spoken Hindi

Both mean the same thing here.

So you may hear:

• गीले कपड़े निचोड़ के बाहर सुखाइए।

But the sentence you were given, with निचोड़कर, is standard and perfectly natural.

Yes. कपड़ा is masculine, and its regular plural is कपड़े.

So:

• कपड़ा = one cloth / one garment
• कपड़े = clothes

This -ा → -े change is very common with masculine nouns in Hindi:

• लड़का → लड़के
• कमरा → कमरे
• कपड़ा → कपड़े

That is why both the noun and the adjective look the way they do:

• गीले कपड़े = wet clothes