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)