1) He didn’t describe the whole day.
2) Perhaps he could have better described the day.
Dice 1) He didn’t describe the whole day. Fine. Dice 2) Perhaps he could have better described the day.
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Dice1) He didn’t describe the whole day.
Fine.
Dice2) Perhaps he could have better described the day.
That works, but more natural is "Perhaps he could have described the day better."
Dice1) He didn’t describe the whole day.
OK.
Dice2) Perhaps he could have better described the day.
Opinions may vary, but I wouldn't entirely recommend this. I would probably understand it as a more formal-sounding alternative to the more usual "Perhaps he could have described the day better". However there may be