The full sentence, which I had to learn was:
わたしは ろくしゅうかんまえに にほんに きました
But I don't understand the meaning of the "-kan" that follows ろくしゅう Can anyone please enlighten me when and why I have to use that suffix?
The かん here is 間 in kanji, and this is used as a suffix to refer to a span of time. ろくしゅう in your sentence is spelled 六週 in kanji and means "six weeks", but in a way that is more ambiguous than the English. Various suffixes can be added on the end to make things more specific, like 目{め} to mean "the sixth week", or 分{ぶん} to indicate six weeks' worth of something, or 間{かん} for a span of time. Have a look partway down the Weblio entry for 間, for sense 1 under the かん reading for some examples of how this かん is used.
ろく
is written as 六
in kanji, you will only occasionally see it written this way. More likely you will just see it as 6週間
.