If the lines $kx+3y+4=0$ and $3x-2y+7=0$ are perpendicular, then the value of $k$ is

Given lines $kx+3y+4=0\cdots \left(1\right)$

$3x-2y+7=0\cdots \left(2\right)$

Slope of equation (1) is $\Rightarrow m_1=\frac{-k}{3}$

Slope of equation (2) is $\Rightarrow m_2=\frac{3}{2}$

Two lines are perpendicular then

$\begin{array}{l}\Rightarrow m_1\times m_2\\ \Rightarrow \frac{-k}{3}\times \frac{3}{2}=-1\\ \Rightarrow \frac{k}{2}=1\\ \Rightarrow k=2\end{array}$