a)\(\left|2x+3\right|\ge0\Rightarrow\left|2x+3\right|+2\ge2\)

The equality happens only when : \(2x+3=0\Leftrightarrow x=-\dfrac{3}{2}\)

b) \(x^2+4x+8=x^2+4x+4+4=\left(x+2\right)^2+4\ge4\)

The equality happens only when : \(x+2=0\Leftrightarrow x=-2\)

Hence,the answers are 2 and 4 respectively