At 15.6 million degrees Celsius the temperature of the sun's core is high enough for nuclear what to occur?

Actually, it is not. The Sun's core is about 28,000,000°F, but it needs to be at least 100 million to undergo nuclear fusion. There are some factors that fusion can occur there. One is density and pressure. The amount of pressure overturns the weak nuclear force which is the force that resists atoms from fusing. Another process known as quantum tunneling provides a sort of "barrier" that helps overcome the weak force and helps force the atoms to fuse.