They're good fun, and I absolutely enjoy to live with them."

I am taking a practice English test for immigration to Canada. I should note that I am a native English speaker from the United States.

During one of the "writing" practice tests, a section appeared asking to circle 10 incorrect words in a text.

One sentence had two incorrect words (the sentence in the title). I found "to live" immediately, but I'm having a hard time understanding why "absolutely" is wrong in this case.

"I absolutely enjoy living with them." sounds correct to me. I'm certain I am missing some grammatical rule that students of ESL would have picked up on, but I'm missing.

Thank you for your help.

This is one of those questions that some (perhaps many) proficient Anglophones would find fault with. One 'error' in the sentence hinges on the acceptability (or not) of the intensifying adverb absolutely in this position, and the acceptability of it modifying the verb enjoy or of it being a 'sentence adverb' modifying the whole clause I enjoy living with them (as certainly can do).

Cambridge English Dictionary gives the sense:

absolutely ...

B1 used for adding force to a strong adjective that is not usually used with "very" or to a verb expressing strong emotion:

• It's absolutely impossible to work with all this noise.
• The food was absolutely disgusting/delicious.
• I absolutely loathe/adore jazz.

The third example shows the construction, with the adverb emphasising the emotion carried by the verb. Normally, the verb rather than the adverb would be stressed in speech, at least in the UK.

The question remains about whether absolutely can acceptably modify enjoy as opposed to verbs carrying more extreme emotions like detest, hate, dote [on].

These Google ngrams indicate that 'I absolutely enjoy' is far less common than 'I absolutely adore', but is not unknown. I'd say it sounds weak, and would not use absolutely with enjoy or like, preferring really. Compare the usage as an intensifier of extreme adjectives: 'absolutely gorgeous', 'absolutely hideous', but not 'absolutely nice'.

.................

Moving from the verb-modifying usage to the clause-modifying usage of absolutely:

Obviously,

• I absolutely eat tomatoes

can only be used with the stress on the adverb, and with the sentence-modifying sense of absolutely:

• Of course I eat tomatoes! / I certainly do eat tomatoes!

And some would label this usage unacceptable in standard English, slang. So much so that it doesn't appear in CED, Lexico, OALD, Collins, AHD, M-W or Macmillan.

So the acceptability of the sentence 'They're good fun, and I absolutely enjoy living with them.' is in the mind of the examiner, sadly.