Hi there! Unfortunately the first sentence is not correct. 'In-depth' is an adjective, so it must always be followed by a separate noun. Here is how your sentence would work correctly with 'in-depth': 'This is an in-depth explanation of the problem' 'This explanation offers an in-depth analysis of the problem.' Here, in both sentences 'in-depth' comes before a noun. If you are looking for a good noun the 'insight' is a good option. It is always 'an insight into something'. With this you can keep your sentence the same: 'The explanation offers an insight into the problem' With the second sentence, everything works, you just need to change the preposition to 'on': 'This explanation throws some light on the question.' Hope this helps!