This question of yours is not well arranged....
In an aptitude test if am given a question like this I wouldn't even solve it because the answer is in the question...
How???
"what is the common difference " then you asked" is it Arithmetic or geometric"
I would have chosen arithmetic because common difference is only typical to arithmetic progression... But this question is a typical Geometric sequence "we use Common ratio"
Common ratio = T₂/T₁
Common difference = T₂-T₁
T₂ = 12 and T₁ =-6
∴Common ratio = 12/-6 = -2......
Meaning each number in the sequence in creases by a factor of -2....
Multiply T₁ by -2 you'll have 12[T₂]
Multiply T₂ by -2 you'll have -24[T₃] and the sequence continues .........
Hope this helped......?