Answer
We can rank the situations in order of magnitude of the particle's acceleration, from largest to smallest:
$e \gt c \gt b = d \gt a = f$
Work Step by Step
Let the electric field $E_0 = 10~N/C$
Let the charge be $q_0 = 1~nC$
Let the mass be $m_0 = 1~pg$
We can find the force on the particle:
$F = E_0~q_0$
We can find an expression for the acceleration:
$a_0 = \frac{F}{m_0} = \frac{E_0~q_0}{m_0}$
We can find an expression for the acceleration in each case.
(a) $a = \frac{(4E_0)~(5q_0)}{(6m_0)} = \frac{10}{3}~a_0$
(b) $a = \frac{(4E_0)~(-5q_0)}{(3m_0)} = -\frac{20}{3}~a_0$
(c) $a = \frac{(8E_0)~(-10q_0)}{(3m_0)} = -\frac{80}{3}~a_0$
(d) $a = \frac{(20E_0)~(-q_0)}{(3m_0)} = -\frac{20}{3}~a_0$
(e) $a = \frac{(30E_0)~(-3q_0)}{(m_0)} = -90~a_0$
(f) $a = \frac{(10E_0)~(-q_0)}{(3m_0)} = -\frac{10}{3}~a_0$
We can rank the situations in order of magnitude of the particle's acceleration, from largest to smallest:
$e \gt c \gt b = d \gt a = f$
