Let a, b, c, d and e be the 5 numbers

The average of a set of five values is 12.
We can write: \(\frac{a+b+c+d+e}{5} = 12\)
Multiply both sides by 5 to get: \(a+b+c+d+e=60\)

If one number is deleted, the average of the set is decreased by 0.6
In other words, if e is deleted, the average of the 4 remaining numbers is 11.4
We can write: \(\frac{a+b+c+d}{4} = 11.4\)
Multiply both sides by 4 to get: \(a+b+c+d=45.6\)

What is the value of the deleted number?
We have:
\(a+b+c+d+e=60\)
\(a+b+c+d=45.6\)

Subtract the bottom equation from the top equation to get: \(e = 14.4\)

Answer: B