Translation:It takes three weeks.
I assume you mean ヶ as in 一ヶ月, not 々 as in 時々. (々 is an ideographic iteration mark, indicating that the previous kanji should be repeated.) The kanji ヶ (pronounced "ka") is apparently a graphical abbreviation of another kanji, 箇, used as a counter for months, places, or provisions.
As for why 間 is used for some spans of time and ヶ is used for others, I don't know.
I've been told that 三日- みっか means the "third day of a month" and 三日間 means the "period of three days". I am still confused about why Duolingo is using it differently though.
Also I've seen people using 間 to count days, weeks, months and years. I don't know if it's exclusive to count weeks.
三日 (みっか) means both "3rd day of the month" and "a period of three days".
3日間 is also "three days" but rather than a length of time (during which something is happening), this indicates a 'frame' of time within which something can happen (often followed by で).
And 間 is indeed a counter for all things time related, from seconds to years - not just weeks.
there is a table in this article with the ones for weeks: