huku ha tiisai danbooru ni, hon ha ookii danbooru ni iremasu.

Because the sentence is setting up two contrasting topics:

• 服は = as for clothes
• 本は = as for books

This use of は often has a contrastive feeling: clothes go in one place, books go in another.

So the sentence is structured like:

• As for clothes, into the small cardboard box
• as for books, into the big cardboard box
• put (them).

Japanese often uses は this way when comparing or separating categories.

Because は is replacing を here.

Normally, with 入れます you might expect:

• 服を入れます
• 本を入れます

But when the object is made the topic or contrastive topic, は can take the place of を:

• 服は
• 本は

So the objects are still the things being put somewhere, but they are being presented as topics for contrast.

A very literal way to think about it is:

• As for clothes, put them in the small box.
• As for books, put them in the big box.

Here, に marks the destination or place something goes into.

So:

• 小さい段ボールに = into the small cardboard box
• 大きい段ボールに = into the big cardboard box

With a verb like 入れます (put in, insert), に commonly marks where the object is placed.

Japanese often avoids repeating a verb when the same verb applies to multiple parts of the sentence.

So instead of saying:

• 服は小さい段ボールに入れます。本は大きい段ボールに入れます。

the sentence combines them and leaves the verb to the end:

• 服は小さい段ボールに、本は大きい段ボールに入れます。

This is very natural in Japanese. The final verb applies to both earlier topic-location pairs.

Because Japanese modifiers come before the noun they describe.

So:

• 小さい段ボール = small cardboard box
• 大きい段ボール = big cardboard box

This is the normal pattern in Japanese:

• 赤い車 = red car
• 新しい本 = new book
• 大きい家 = big house

In everyday Japanese, 段ボール often refers to a cardboard box, not just the material.

So in this sentence, 小さい段ボール and 大きい段ボール are naturally understood as:

• small cardboard box
• big cardboard box

If you translated it as just cardboard, it would sound odd with に, because に here suggests putting something into a container.

It is one sentence, but it contains two parallel parts:

• 服は小さい段ボールに
• 本は大きい段ボールに
• 入れます

You can think of it as two instructions compressed into one:

• Put the clothes into the small cardboard box.
• Put the books into the big cardboard box.

Japanese often joins parallel information like this and gives the verb once at the end.

Japanese nouns usually do not show singular vs. plural the way English nouns do.

So:

• 服 can mean clothes or a piece of clothing, depending on context
• 本 can mean book or books

In this sentence, the natural reading is probably plural:

• clothes
• books

But the grammar itself does not force that.

The comma helps separate the two contrasted parts of the sentence and makes it easier to read:

• 服は小さい段ボールに、
• 本は大きい段ボールに入れます。

It shows a pause between the two parallel items. Japanese commas are often used more flexibly than English commas, so this is mainly for clarity and rhythm.

Yes, that is possible, but the nuance changes.

• 服を小さい段ボールに、本を大きい段ボールに入れます
  This is more neutral: it simply states what goes where.

• 服は小さい段ボールに、本は大きい段ボールに入れます
  This has more of a contrastive feel: clothes go in the small box, books go in the big box.

So は is useful when you want to emphasize the distribution or comparison between the two categories.

Because Japanese and English organize sentences differently.

English often goes:

• Subject + verb + object + place

Japanese often puts the verb at the end, and information before it can be arranged based on topic and emphasis.

Here the sentence builds up the categories and destinations first, then finishes with the action:

• 服は = as for clothes
• 小さい段ボールに = into the small box
• 本は = as for books
• 大きい段ボールに = into the big box
• 入れます = put

So the sentence may feel backward from an English perspective, but it is a normal Japanese pattern.