To factor the expression \(36 - y^2\), we recognize that it is a difference of squares. The difference of squares can be factored using the formula:
\[ a^2 - b^2 = (a - b)(a + b) \]
In this case, we can identify \(a^2 = 36\) and \(b^2 = y^2\). Thus, we have:
\[ a = 6 \quad (\text{since } 6^2 = 36) \] \[ b = y \]
Now we can apply the difference of squares formula:
\[ 36 - y^2 = 6^2 - y^2 = (6 - y)(6 + y) \]
Therefore, the completely factored form of \(36 - y^2\) is:
\[ \boxed{(6 - y)(6 + y)} \]