How to host a subdoman and main domain in a same droplet?

I have a droplet in Ubuntu 14.04,what I want to do is create a subdomain and host it in the same droplet.

My main domain : example.com Subdomain created : api.example.com

**What I tried so far: **

1. Created a “A” record for api.example.com in Networking section

2. Created a CNAME record for www.api.example.com

3. Set up the virtual host for api.example.com following this How To Set Up Apache Virtual Hosts on Ubuntu 14.04 LTS

**Below is the step I tried to set up the virtual host **

1. The droplet is installed Apache2 before,so I didnt install again

2. Create the directory for my api.example.com by using this command sudo mkdir -p /var/www/api.example.com/public_html

3. Create a demo page by using this command nano /var/www/api.example.com/public_html/index.html and add a simple html code inside it .

4. I copy the 000-default.conf to my new created conf like this sudo cp /etc/apache2/sites-available/000-default.conf /etc/apache2/sites-available/api.example.com.conf

5. I change the api.example.com.conf to the following:

<VirtualHost *:80>
    ServerAdmin myemailaddress@example.com
    ServerName api.example.com
    ServerAlias www.api.example.com
    DocumentRoot /var/www/api.example.com/public_html
    ErrorLog ${APACHE_LOG_DIR}/error.log
    CustomLog ${APACHE_LOG_DIR}/access.log combined
</VirtualHost>

6. Lastly I use this command to enable the virtual host for api.example.com sudo a2ensite api.example.com.conf and restart the apache by sudo service apache2 restart

After all this step, I test my subdomain,but it doesnt work.It said refused to connect

so what I missing here?? Can somebody help??