kono sentakukago ha mitame hodo ookiku nai keredo, taoru ha takusan hairimasu.

洗濯かご is a compound noun:

• 洗濯 = laundry
• かご = basket

So together it means laundry basket.

Japanese often combines nouns directly like this, especially for common objects. 洗濯のかご is not impossible, but 洗濯かご sounds more like the normal dictionary-style name of the item.

この modifies the whole noun phrase 洗濯かご.

So:

• この洗濯かご = this laundry basket

Even though 洗濯かご is made of two nouns, it functions as one unit, so この goes before the whole thing.

見た目 means appearance or how something looks.
ほど in this pattern means to the extent that or as much as.

So:

• 見た目ほど大きくない = not as big as it looks
• literally, not big to the extent its appearance suggests

This is a very common pattern:

• Aほど Bない = not as B as A

Examples:

• 思ったほど難しくない = It’s not as difficult as I thought.
• 見た目ほど重くない = It’s not as heavy as it looks.

Because 大きい is an い-adjective, and negative forms of い-adjectives are made by changing -い to -くない.

So:

• 大きい = big
• 大きくない = not big

This is the normal rule:

• 高い → 高くない
• 新しい → 新しくない
• 面白い → 面白くない

So 見た目ほど大きくない is grammatically the correct way to say not as big as it looks.

けれど means but, although, or though.

It connects two ideas:

1. This laundry basket is not as big as it looks
2. But it can hold a lot of towels

So the sentence shows a contrast:

• it does not look very big,
• however, it holds a lot.

In casual English, this is like:

• It’s not as big as it looks, but it holds a lot of towels.

They do different jobs in the sentence.

1. この洗濯かごは

This は marks this laundry basket as the main topic.

2. タオルは

This second は highlights towels within the second clause.

It gives a nuance like:

• As for this laundry basket, it’s not as big as it looks, but as for towels, a lot fit in it.

This second は can feel contrastive or selective:

• maybe towels fit easily,
• perhaps other things might be different.

Japanese often uses は more than once in a sentence to organize information.

入る basically means to go in / to enter / to fit inside.
Its exact translation depends on context.

Here, the subject is タオル:

• タオルはたくさん入ります
  = A lot of towels fit in it
  = It can hold a lot of towels

So Japanese is focusing on the towels as the thing that goes in.

This is very natural with containers:

• この箱には本がたくさん入る = A lot of books fit in this box.
• このバッグにはノートパソコンが入る = A laptop fits in this bag.

So 入る is often used where English uses fit or hold.

Yes. Japanese often leaves out information that is obvious from context.

Here, what is omitted is basically:

• in this laundry basket
• or inside it

A fuller version could be something like:

• この洗濯かごには、タオルがたくさん入ります。

But because the basket has already been introduced as the topic, Japanese does not need to repeat it.

So the sentence naturally means:

• This laundry basket isn’t as big as it looks, but a lot of towels fit in it.

たくさん means a lot or many.

In タオルはたくさん入ります, it means:

• many towels fit
• it holds a lot of towels

So たくさん is describing the quantity of towels that can go in.

It is placed before the verb, which is very common in Japanese:

• 本がたくさんある = There are a lot of books.
• 人がたくさん来た = A lot of people came.

Good question. These are different verbs:

• 入る = to go in / to fit
• 入れる = to put in

So:

• タオルはたくさん入ります
  = A lot of towels fit in it

But:

• タオルをたくさん入れます
  = I put a lot of towels in it

This sentence is not talking about someone actively putting towels into the basket. It is talking about the basket’s capacity, so 入る is the natural choice.

Because the whole sentence is written in the polite style.

You can see that in:

• ないけれど
• 入ります

The plain version would be:

• この洗濯かごは見た目ほど大きくないけど、タオルはたくさん入る。

The meaning is the same, but the original sentence sounds more polite and neutral, which is common in textbooks and everyday careful speech.