You chose to bid 4 Spades. This is the correct answer. I think it is justified by your point count and the good 8 card fit in Spades.

The bidding then continues, and East No Bids, South No Bids, and West, considers whether to Double or not.  Here is West's  hand. You can see 4 probable winners, but when you are in a suit contract, what you have to worry about is getting trumped if the other side are short of your suit. By making a Takeout Double, you expect North to have a shortage in Hearts, so you can't really count on your King as a trick. I don't think it would be wise to double.

Spades        A,Q,4
Hearts         K,10,9,8,7
Diamonds    A,J,6,5
Clubs           9
 

I think you should now play out the hand, and see if you can make 4 Spades.

West leads to the first trick, and one possibility would be to lead his Singleton, the 9 of Clubs. A singleton is often a good lead, especially if your partner can win the trick and play the suit back to you, for you to trump in straight away.
 

If you have problems with the hand and want to see how to play it out, click here.

With the successful completion of that hand, the rubber is over. What is the final score?

Now go on to Lesson 9, which is about Pre-empive Bids.