\((a+b)^2=a^2+2ab+b^2\ (*)\\-------------------\\\\k^2+8k+12=0\ \ \ \ \ |subtract\ 12\ from\ both\ sides\\\\k^2+8k=-12\\\\k^2+2\cdot k\cdot4=-12\ \ \ \ \ |add\ 4^2=16\ to\ both\ sides\\\\\underbrace{k^2+2\cdot k\cdot4+4^2}_{use\ (*)}=-12+16\\\\(k+4)^2=4\iff k+4=\pm\sqrt4\\\\k+4=\pm2\Rightarrow k+4=2\ or\ k+4=-2\ \ \ \ |subtract\ 4\ from\ both\ sides\\\\\boxed{k=-2\ or\ k=-6}\)