The number of spectral lines emitted, during transition is, n(n-1)/2
=> 6 =n/n(n-1)
=> 12= n2-n
=> n2 - n -12 =0
=> n2 - 4n -3n-12 =0
=> n(n-4) + 3(n-4) = 0
=> (n+3(n-4) = 0
n = -3,4
Considering positive value, we have n=4
Now, \(\frac{1}{\lambda}=R(\frac{1}{1^2}-\frac{1}{4^2})\)
=> \(\lambda\) =16/15R= 975 Å