The first thing you want to do is make sure the computers you are going to ping are in the same network neighborhood. In the following photo, I will show you how to check on both computers to see what your ipv4 and ipv6 addresses. For the IPV6 address you want to choose the link local ipv6 address. To check your ipv4 and 6 address type ipconfig at the command line.
To manually input your ipv4 and 6 addresses go to network and sharing center. From there go to change adapter settings, and right click and go to properties, from there left click on properties ipv4 and ipv6 addresses and click use the following ip address and press tab to get the subnet mask. Do not worry about configuring the default gateway.
After this step you will want to ping each host ipv4 and 6 addresses. I will demonstrate with the next photos on how to ping each address. http://www.howtogeek.com/howto/19249/how-to-assign-a-static-ip-address-in-xp-vista-or-windows-7/ . That link is to show how to assign a static ip address. The first two photos are of my toshiba pinging my acer and the last two are my acer pinging my toshiba computer.
The next photo will show you how to ping yourself by testing the loopback address. To do this ping and type 127.0.0.1.
This next photo shows me pinging the website I used to learn how to assign a static IP address.