Maximum frictional force between $\mathrm{A}$ and $\mathrm{B}$ could be

${\mathrm{f}}_1={\mathrm{\mu }}_1{\mathrm{m}}_{\mathrm{A}}\mathrm{g}=\left(0.2\right)\left(2\right)\left(10\right)\mathrm{ }\mathrm{N}$

${\mathrm{f}}_1=4\mathrm{ }\mathrm{N}$

Acceleration when frictional force is maximum,

$\mathrm{a}=\frac{{\mathrm{f}}_1}{{\mathrm{m}}_{\mathrm{A}}}$

$\mathrm{a}=\frac{4}{2}=2\mathrm{m}/{\mathrm{s}}^2$

Fictional force between ground and B

${\mathrm{f}}_2={\mathrm{\mu }}_2\left({\mathrm{m}}_{\mathrm{A}}+{\mathrm{m}}_{\mathrm{B}}\right)\mathrm{g}$

${\mathrm{f}}_2=0.4\left(2+4\right)\left(10\right)$

${\mathrm{f}}_2=24\mathrm{ }\mathrm{N}$



Therefore for the entire system,

$\mathrm{F}-{\mathrm{f}}_2=\left({\mathrm{m}}_{\mathrm{A}}+{\mathrm{m}}_{\mathrm{B}}\right)\mathrm{a}$

$\mathrm{F}-24=\left(2+4\right)\left(2\right)$

$\mathrm{F}=36\mathrm{ }\mathrm{N}$