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Sir,

1. She spent her days cooking food.

here

She =subject
spent=verb
indirect object=her days

cooking=?

2. She spent her days to cook food.

Why "to cook" is not possible here.

Thanks.
Comments  
Sentence 1 is correct: the phrase is 'to spend time' + gerund.

'Cooking' here is the gerund.
Hello,

He spent her days making money.

he=sub
spent =verb
her days=Ind. obj.
making money=?

Thanks.
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He spent his days making money.

he = subject
spent = verb
his days = Direct object (What did he spend? - his days)
making money = adverbial phrase of manner (How did he spend his days? - making money)
Sir,

He spent her days making money. ok.

He spent her days to make money.

why "to make " is not possible.

Thanks.
- He spent her days to make money.

IMHO, this means;
In order to make money, he spent her days.

Therefor, it doesn't make sense.

Am I right, teachers?
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Hanuman, the construction here is:

'to spend [unit of time] + gerund + object of gerund', e.g.

'to spend [the weekend] + drinking + beer'
'to spend [an hour] + watching + television'

Some verbs are followed only by the gerund, some by the infinitive, and some by either the gerund or the infinitive. Unfortunately, you have to learn the correct constructions one by one, as there isn't a reliable rule.

This construction takes the gerund, and so 'to make' isn't idiomatic.

Jandi, I understand what you mean, when you replace 'to' with 'in order to'. As you have discovered, the sentence then doesn't make sense. This is because the phrase 'he spent his days' requires a 3rd element: 'the way in which he spent them'.