Squatting through a full range of motion like you see in the picture is an excellent way to build balance, flexibility, and strength, but some people don’t have as much natural aptitude as others for developing the ability to perform the movement. Fortunately, the prescription for developing this ability is fairly straight forward.
A lot of people develop the erroneous perspective that the lack of flexibility comes from their back or hips, but for most people the lack of flexibility actually comes from their ankles. The way to advance to squatting deeper is to focus on your feet and your ankles.
Make sure you set your feet so they are pointing out in front of you at a 45 degree angle. The way you get yourself all the way down so that the back of your thighs are touching your calves while maintaining a flat back is you set some kind of stable object like a weight plate or a 2 x 4 under your heels. It shouldn’t need to be more than a couple of inches tall.
Perform squats using this support for about a month then switch it out for something that is only about one inch tall and perform squats using the one inch support for a month and after that you should be able to perform squats all the way down without any support.