Music is life

There are in total 3 cases to choose 4 albums, such that all 3 bands are represented:

• Selecting 2 albums of GP, 1 of LP and 1 of C. Hence the total number of cases comes out to be 6C1 * 3C1 * 2C2=18
• Selecting 2 albums of LP, 1 of GP and 1 of C. Hence the total number of cases comes out to be 6C1 * 3C2 * 2C1=36
• Selecting 2 albums of C, 1 of LP and 1 of GP. Hence the total number of cases comes out to be 6C2 * 3C1 * 2C1=90

Adding the above possible cases we get a total of 144 cases. And we've got our answer :)

There are three possible cases:

Case-I
Selecting 2 album of Coldplay, one of Linkin Park and one of Green Day

Number of Cases: $\binom {6} {2}$ * $\binom {3} {1}$ * $\binom {2} {1}$ $=90$

Case-II
Selecting one album of Coldplay, 2 of Linkin Park and one of Green Day

Number of Cases: $\binom {6} {1}$ * $\binom {3} {2}$ * $\binom {2} {1}$ $=36$

Case-III
Selecting one album of Coldplay, one of Linkin Park and 2 of Green Day

Number of Cases: $\binom {6} {1}$ * $\binom {3} {1}$ * $\binom {2} {2}$ $=18$

Hence, Total Cases $= 90+36+18=$ $\boxed{144}$