Solution:

Let \(x\) be the first part and \(y\) be the second part.

\(x+y = 80\)

\(\frac{x-4}{y-8}=\frac{1}{3}\)

\(3(x-4) = y-8\)

\(y = 80-x\)

\(3(x-4) =80-x-8\)

\(3x+x = 72 +12\)

\(x = 21\)

\(y = 80-21 = 59\)