A 難問 is difficult question. Here is an extract of the kanji entries.
難
[音] ナン
[訓] かた.い -がた.い
むずか.しい むづか.しい
むつか.しい -にく.い[英] difficult; impossible; trouble; accident; defect
問
[音] モン
[訓] と.う と.い とん
[英] question; ask; problem
There is a similar word, 難読, read as なんどく, with the second kanji giving more a meaning of ‘difficult to read’. This is generally in the context of kanji that are hard to read because they are rare or obscure. Words in which this appears include
難読地名【なんどくちめい】 difficult place-name to read
難読漢字【なんどくかんじ】 difficult kanji to read
Looking through lists of 難読漢字 are good ways to test your abilities but obviously require a lot of prior kanji study. However the reality of being in Japan means there is a lot of difficult kanji to read and so effective practice is vital.
Another good way to get in such practice is to pay attention whenever you’re travelling, as train stations will have their name with furigana above. I used to try and visualise how a train station name would be done in kanji and then look at the sign to check my guess. I did something similar when working at a hotel in Japan, which was to cover the section which showed the reading of the name and then try and read the names on reservations.
In the end, you need to put yourself out there and try and read everything! Engage your brain as much as possible and never be content with passively reading things. It is very important to test your knowledge by asking Japanese people how things are read. I used to carry a physical flashcard in my pocket with the following phrase:
この漢字の読み方を教えてください。
I would also have a small notebook that I would write these things down (or even better, get the Japanese person to write it to make sure I didn’t make some silly transcription mistake).
Make sure you are trying to put your skills into action and are not just nosedeep in textbooks all day.
