Concept: The question deals with fundamentals of inequality and sign change.
Solution:
6/a(a+1)  > 1 and this is not possible for a(a+1)<0  

=> a(a+1) >0 and in other words it implies a(a+1) is positive.

=>6 and 1 are positive values too and hence we can now confidently write 
6/a(a+1) >1 => 6>a(a+1)

=>a(a+1)<6

=>a^2 + a <6

=>a^2 + a -6 < 0  (Add -6 on both sides)

=>a^2 +3a - 2a -6 < 0
=> a(a+3) - 2(a+3) <6
=> (a+3)(a-2) < 6

Use the wavy line approach now to reach the critical points as -3 and 2,plot them on the number line and consider the negative interval values only
=> +.................(-3).................  -  ...................(2)...............+...

 NEGATIVE INTERVAL To be considered AS "<" sign in inequality

=>        -3<a<2  and the only option satisfying the range is -2.5 (option b)