The number of listens for FM sister station = 26,000
The number of listens for AM radio station = 156,000
Explanation:
The total number of listeners of both station combined = 182,000
Let us assume the number of listens for FM sister station = M
So, the number of listens for AM radio station
= 6 x ( number of listens for FM sister station ) = 6 M
Now,as given,
The number of listener for (AM radio station + FM sister station ) = 182,000
⇒6 M + M = 182,000
or, 7 M = 182,000
or,

⇒ M = 26,000
Hence, the number of listens for FM sister station = M = 26,000
The number of listens for AM radio station
= 6 M = 6 x(26,000) = 156,000