Factor. \[ 9 y^{2}+24 y+16 \]

Step 1 ：This is a quadratic equation in the form of \(ax^2 + bx + c\). The equation can be factored if it satisfies the condition \(b^2 - 4ac = 0\). If this condition is satisfied, the equation can be factored into \((px + q)^2\), where \(p\) and \(q\) are constants.

Step 2 ：The expression \(9y^2 + 24y + 16\) is factored into \((3y + 4)^2\).

Step 3 ：Final Answer: \(\boxed{(3y + 4)^2}\)