Hey Julian!
We know that there is at least one day on which both J and H are assigned and because K is assigned to Tuesday and Friday, those are not days where J and H could both go. Here's where it pays to explore. If you run out the JH chunk on Wednesday as the two frames above place the JH chunk on either Monday or Thursday, the problem you run into is that since the Ls are consecutive and the Gs are not, there's no way to get them on the diagram without G and L overlapping at least once.
Thus there are only two places for the JH chunk, which was the split used in the frames above. If the JH chunk is on Monday, then in order to separate the Gs while keeping the Ls consecutive, Ls must be assigned to both Wednesday and Thursday, with Gs on Tuesday and Friday. If the JH chunk is on Thursday, then the Ls must go on either Monday and Tuesday, or Tuesday and Wednesday (outlined in the second frame).
You can also do this game without frames using the diagram below.
Hope that helps!