To factor the expression \(36x + 8y\), we can start by finding the greatest common factor (GCF) of the coefficients of the two terms.
- The coefficients are 36 and 8.
- The GCF of 36 and 8 is 4.
Now, we can factor out the GCF from the expression:
\[ 36x + 8y = 4(9x + 2y) \]
Thus, the factored form of the expression is:
\[ \boxed{4(9x + 2y)} \]