From the definition of the conditional probability,
\(\displaystyle{P}{\left({B}{\mid}{A}\right)}=\frac{{{P}{\left({A}\ {\quad\text{and}\quad}\ {B}\right)}}}{{P}}{\left({A}\right)}\)

So, \(\displaystyle{P}{\left({A}\ {\quad\text{and}\quad}\ {B}\right)}={P}{\left({A}\right)}{P}{\left({B}{\mid}{A}\right)}={0.6}\cdot{0.4}={0.24}\)

So, \(\displaystyle{P}{\left({A}\ {\quad\text{and}\quad}\ {B}\right)}={P}{\left({A}\right)}{P}{\left({B}{\mid}{A}\right)}={0.6}\cdot{0.4}={0.24}\)