Answer
$m_A = 6.7 ~kg$
Work Step by Step
If there is no motion, then the acceleration is zero.
Let's consider the force equation for $m_A$:
$\sum F = ma$
$F_T - F_f = 0$
$F_T = F_f$
Let's consider the force equation for $m_B$:
$\sum F = ma$
$F_T - (m_B)g = 0$
$F_T = (m_B) ~g$
We can use the force equation for $m_A$ to replace $F_T$ with $F_g$.
$F_f = (m_B) ~g$
$(m_A)(g)(\mu_s) = (m_B) ~g$
$m_A = \frac{m_B}{\mu_s} = \frac{2.0 ~kg}{0.30} = 6.7 ~kg$
If box A has a mass of 6.7 kg, then no motion will occur.
