$($calculator not allowed$)$

Let $g$ be a twice$-$differentiable function with $g^{\text{'}}(x)>0$ and $g^{\text{'}\text{'}}(x)>0$ for all real numbers $x,$ such that $g(4)=12$ and $g(5)=18.$ Of the following, which is a possible value for $g(6)?$

$($A$)15$

$($B$)18$

$($C$)21$

$($D$)24$

$($E$)27$