This version of printing is what as know as simulated studio.  It uses up to 8 different additive primaries along with black and white to generate something that can look like an array of tons of colors.   We use tiny dots of each color - known as halftones - that are then aligned and printed atop one and other to create the perfect blend of colors.  This style of printing can be used for both illustrative design such as this, but also to generate more photographic images.  We can use this printing style on any color shirt and it always generates a great image and is very versatile.  The downside is that it can be pretty expensive - both in set-up and per piece - due to the use of a lot of screens.  Also you cannot generate exact color matches using this method.  If you need specific pantones matched we would have to either generate a perfect spot on top of this or utilize spot color printing.