Answer
$a = 4$ $m/s$
Work Step by Step
Using eqn:$ $ $ x = x_{o} + V_{o}t + \frac{1}{2}at^{2}$
Solution when t=1s and x=0:
$ x = x_{o} + V_{o}t + \frac{1}{2}at^{2}$
$ 0 = -2m+ (V_{o}\times 1s) + (\frac{1}{2}\times a\times(1s)^{2})$
$2 =V_{o} + \frac{1}{2} a$ ..............................(1)
Solution when t=2s and x=6m:
$ x = x_{o} + V_{o}t + \frac{1}{2}at^{2}$
$ 6m = -2m + (V_{o}\times 2s) + (\frac{1}{2}\times a\times (2s)^{2})$
$8 = 2 V_{o} +2a$
$4 = V_{o} +a$ ..............................(2)
Solving the simultaneous eqn:
$4 = V_{o} +a$ ..............................(2)
$2 =V_{o} + \frac{1}{2} a$ ..............................(1)
Subtract the 1st eqn from the 2nd eqn and you get:
$2 = \frac{1}{2} a$
$a = 4$ $m/s$
