Translation:Sorry, I do not have time. I cannot go.
Because another way of saying: “I can’t go” (to a party or a gathering, even a conference) in English is: “I can’t make it” (to the party/gathering/conference). The latter is more often used as part of an apology. It implies that you want to and put some effort in but just can’t manage to make the timing work etc.
Reported: "Sorry, I'm not available, I cannot go." is not accepted, despite "not available" being a proposed translation in the hover text.
It rejected "Sorry, I don't have time, so I can't go"--because of the "so." It is true that there is no overt "so" in the Chinese, but the meaning is implicitly there.
Yes, in other exercises Duo even uses "so" to join the two clauses together in English where the Chinese just uses a comma splice, so they really shouldn't mark you wrong if they do it themselves. However some other posters here have been rejected for saying "don't" and "can't" so that could be the reason you were marked wrong rather than the "so".
不能去 here means "I cannot make it" instead of "I cannot go".
I feel confused with it. Can you explain it? Is it a kind of an idiomatic expression?
Yes. “I can’t make it” is English idiom for not being able to attend something.
"Sorry, I don't have time. I'm unable to go." should be accepted; the suggested answer "sorry [sic], I don't have time. I cannot go." has an identical meaning (and needs a capital letter "S").
So is this three thoughts joined by commas a standard Chinese grammar thing that is acceptable in that language, or is Duolingo just being careless? In English This would be at least two sentences joined with a semicolon. I'm sorry. I have no time; I cannot go. 8/28/18
Yes the comma splice is commonly used in Chinese apparently. Here is a brief Wikipedia extract:
The comma is used to join together clauses that deal with a certain topic or line of thinking. As such, what would appear to an English speaker to be a comma splice is very commonly seen in Chinese writing. Often, the entirety of a long paragraph can consist of clauses joined by commas, with the sole period coming only at the end.
"Sorry, I'm not free and can't go" corrected to "Sorry, I'm not free. I can't go."
Why do you want a colloquial paraphrasing when the literal translation fits perfectly?
You are correct in saying that "I cannot go" is correct, but "I cannot make it" is hardly colloquial. It is a universally established expression in English.
Yes, it is colloquial; an expression used in common everyday conversation - not formal. Being "universally established" doesn't change that.