You chose to bid 3 Spades. This is correct.
Your losing trick count was 6 (3 Spades, 1 Heart, and 2 Diamonds) and you opened the bidding with your 5 card suit even though you have only low cards in it, and bid 1 Spade.
Your partner has 9 losers (2 Spades, 3 Hearts, 3 Diamonds, and 1 Club) so can give you a supporting bid of 2 Spades.
Now that you add your losers, 6, to your partner's losers, 9, you get 15. Subtracting 15 from 18 makes 3 so your combined hands should be worth a bid of 3 Spades.
Now let's play out those 2 hands, and see if you can make the contracts promised.
Click here to see the cards for Hand One.
Click here to see the cards from Hand Two.
If you had any difficulty in making the contracts as bid, click here for Hand One, and here for Hand Two.
Before we leave the subject of the Losing Trick Count, let me remind you that it is of most use when you and your partner are bidding in the same suit. Although you should always be aware of your losing trick count, if you and your partner do not have a suit fit, it is not of much use to you.
Remember that you do not use the losing trick count at all when you are bidding in No Trump except to say that with an opening hand such as the one below:
Although you have 12 points, which should be sufficient for a 1 No Trump opener, with having 9 losers, I would No Bid on that hand. I would open a 1 No Trump with 8 losers, however.
If you are considering being an overcall bidder, I would think you should have no more than 8 losing tricks to overcall, and your partner should also have no less than 8 losers to support you.
Let's have an example hand to clarify what I mean by this.
Let's say the Opening bidder who was North opened with 1 Club.
This is your hand as East
You have 8 losers, but I think it is worth an overcall bid of 1 Heart. Let's say the partner of the opening bidder said 2 Clubs.
Now let's say your partner West has this hand:
55. What should West bid on this hand?
a. 2 Diamonds
b. 2 Hearts
c. No Bid