Step-by-step Solution:

The idiomatic phrase a hard nut to crack refers to a problem, situation, or task that is very challenging or difficult to solve. Let us analyze the options:\[\] (a) an interesting problem - This is incorrect because the phrase does not refer to something merely interesting. \[\] (b) a difficult problem - This is the correct choice as it directly matches the meaning of the idiom. \[\] (c) a unique problem - While unique problems can be challenging, the idiom specifically refers to difficulty, not uniqueness. \[\] (d) a simple problem - This is incorrect because a hard nut to crack \(\implies\) difficulty, not simplicity. \[\] \[\] Correct Answer: (b)