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Horizontal acceleration of the system is $a=\large\frac{F}{m+2m+2m}$

$\qquad=\large\frac{F}{5m}$

Normal force between B and C is N

is given by $N=2m \times a$

$\qquad=2m \times \large\frac{F}{5m}$

$\qquad=\large\frac{2}{5}$$F$

B will not slide down if frictional force is more that the weight mg of block B

$\mu \geq mg$

$\mu \large\frac{2}{5} $$F \geq mg$

$F \geq \large\frac{5}{2 \mu}$$mg$

Hence b is the correct answer.

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