A、(x-12)(x+2)=x2+2x-12x-24=x2-10x-24,故本选项错误;B、(x+12)(x-2)=x2-2x+12x-24=x2+10x-24,故本选项正确;C、(x+4)(x+6)=x2+6x+4x+24=x2+10x+24,故本选项错误;D、(x-4)(x-6)=x2-6x-4x+24=x2-10x+24,故本选项错误;故选B.