Why is the を particle used twice here

Question

I came across this sentence in the basic kanji book

くつを一足とくつ下を四足買いました

The sentence has two を particles even though I thought the を particles can only be used once in a sentence. I thought since the と particle connects two nouns together it would look like this:

くつの一足とくつ下の四足を買いました

Is this not possible or is the whole grammar wrong? Why is it like that?

Answer 1

This を particle does not necessarily represent the object marker. Let's explore why.

くつを一足　(one pair of shoes)

This を is used in connection with counters. It does not necessarily indicate a direct object here. According to the answer found here (and here), when working with counters, you can use the following structure:

(Noun) (Particle) (Number + Counter) (Verb/Verb Phrase)

But where is the verb in this case? So far, we have Noun を Number + Counter but no Verb. This is because there is yet another noun used in relation to the verb. (You aren't just buying a pair of shoes, you're also buying a pair of socks.)

The key here is the fact that there is a と in this sentence. In this case, と is used for making a list--translated to and in this case.

I want to make a special note that くつを一足 is a noun phrase. In other words, it acts like a single noun in terms of sentence creation. The same goes with くつ下を四足. These both combine to be the direct object. This grammar structure is not uncommon, as you will see in the other answers above, but a good rule of thumb goes like this:

(Noun) (Particle) (Number + Counter) と (Noun) (Particle) (Number + Counter) (repeat if necessary)+ (Verb/Verb Phrase)

くつを一足とくつ下を四足 + Verb Phrase (one pair of shoes and four pairs of socks + verb phrase)

So what's the direct object? In this case, it's the part of the sentence just above in yellow. One pair of shoes, and four pairs of socks is our direct object.

We are combining two different ideas into one sentence here:

くつを一足買いました。

くつ下を四足買いました。

Putting it together, we can either say:

くつを一足とくつ下を四足買いました。

くつ下を四足とくつを一足買いました。

Should we include the counters as part of the direct object? Well a direct object applies to a noun. The phrase noun+number+counter is a noun phrase, acting as a noun. So I would say yes.

Hope it helps.

Answer 2

Your version is possible, but we don't usually say it in that way.

くつを一足とくつ下を四足買いました。

一足のくつと四足のくつ下を買いました。

These two are natural.

When we say '一足買いました,' this 一足 is an adverb. In other words, we don't buy something named '一足'.

くつを一足買いました。[一足 in 一足買う is an adverb]

一足のくつを買いました。[一足の is an adjective]

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[Edit to add]
I've noticed I haven't answered the title question.

Why is the を particle used twice here

That is because each of these nouns (くつ and くつ下) is needed to be indicated as the object of the verb.
I parse the sentence as two adverb phrases connected with と.

[くつを一足 (adv)] と [くつ下を四足 (adv)] 買いました。

When we have two items as the subject of a verb, we say

くつが一足 と くつ下が四足 あります。

くつを一足 or くつが一足 alone doesn't stand very good as a noun to native's ears, and is needing a verb.

▶ You can also say it as follows; without the particle in the middle, くつ一足、くつ下四足, they become nouns, and you need the particle, を, once, right after the whole phrase.

くつ一足とくつ下四足(と)を買いました。[the second と is usually omitted]

But when it's くつを 一足 買いました, this 一足 is an adverb modifying the verb, 買いました.

Cf:「子供が３人遊んでいる」「夏休み中に小説を10 冊読んだ」の中の数量名詞も、その働きは副詞的である。
(Source: 日本語教師のページ | 名詞の副詞的用法)

Also see: How to say "a year has 12 months"?