I want to get a motorola moto x (2nd generation) but I am unsure if the phone can work in other countries outside of the United States, specifically China.
According to the spec sheets, YES, a Moto X 2014 will work in China at 3G speeds.
China provides access to their GSM network over the 2100MHz (HSPDA, or 3G) and 2500MHZ (LTE) spectrums, shown here. A Motorola Moto X (2nd Gen) purchased in the United States (from either Verizon or AT&T) covers that 2100MHz band for 3G, but doesn't touch the 2500MHz for LTE, as seen here. In fact, the spec sheet shows it should work, to some degree, almost anywhere in the world that provides GSM service.