I asked himhow he solved the problem. The underlined clause is a/an -

I asked him how he solved the problem. The underlined clause is a - Noun clause.
• A noun clause is a group of words that band together and act like a noun.
- Nouns clauses are used when a single word isn't enough. They're always dependent clauses.

• একটি বাক্যের চারটি স্থানে Noun clause  বসতে পারে-
1. subject হিসাবে 
2. transitive verb এর object হিসেবে
3. Linking verb এরপরে complement হিসাবে 
4. Preposition এরপরে

• প্রদত্ত বাক্যে 'how he solved the problem" clause টি transitive verb এর object হিসাবে বসেছে, তাই এটি Noun clause.