- den här = denna = this, singular en-word
- det här = detta = this, singular ett-word
de här = dessa = these, plurals
den där = den (with emphasis) = that, singular en-word
- det där = det (with emphasis) = that, singular ett-word
- de där = de (with emphasis) = that, plurals
Note also that den/det/de här always take the definite, while denna/detta/dessa always take the indefinite.
It is always ok but there's a small subtle difference.
In this sentence, we only express that "the knives we are talking about are the cooks'". If let's say we are in the kitchen, pointing at the knives, we would say "De är våra kockars knivar". We are being much more specific when using "den". "Det" refers more to the "state of things" while "de" would refer to the knives themselves.
This is one of those things that us native speakers don't even think about and you will probably understand this a lot more with practice.
Duolingo has a bug that shows answers with plural apostrophes as incorrect or typos. When that happens, it shows the default translation regardless of what you entered. We do accept "Those are our cooks' knives" as well. I'm guessing either that's what happened, or your typo "kinives" caused the sentence to be marked incorrect.
I'm confused by the English translation of this sentence as is kockars plural or singular... the English translation suggest that the kockars is plural as the apostrophe is in the wrong place for a singular object in the English translation e.g....
"They are our cook's knives" = "They are the knives belonging to our cook" where as "They are our cooks' knives" = "They are the knives belonging to our cooks" (cooks being more than one cook) - also if it is supposed to mean more than one cook then in the clicking text options that adds to the confusion as the words available to clicking text doesn't include the ' just cooks.