There are a couple ways to tackle this. The team is looking for a design to use on a new series of tshirts, hoodies, etc. Ideally, it would be a design that folks are happy to wear to the office, but also subtle or stylish enough that you'd be proud to sport it casually on the street too.
A good, safe design will likely be clean, minimal, and smallish, and would fit in the corner of a t-shirt or hoodie. It would draw from design principles common to Google products, like an emphasis on primary colors a white background. Something as simple as a modified version of our homepage logo and title (http://www.google.com/chrome) that says "chrome sync" or "think sync" (the team's slogan) would be a good starting point.
A great design will take those same common design principles, but go bolder. It might include an abstract/futuristic graphic that incorporates the concepts around Sync (the web, data swirling in motion, information ubiquity), a stylized chrome logo, etc. It could be light and colorful or dark and hacker-esque. It might take up more of the front of a t-shirt or hoodie, with the brand taking a backseat or subtle integrated into the graphic design itself.
For reference, the official google font/color is General GG or Open Sans and #03c. If you happen to include font, it should probably be one or both of those (or something close).