Factor. \[ m^{2}+12 m+36 \]

Step 1 ：To factor the quadratic expression \(m^{2}+12 m+36\), we need to find two numbers that multiply to 36 (the constant term) and add to 12 (the coefficient of the middle term).

Step 2 ：The numbers that satisfy these conditions are 6 and 6, because \(6 \times 6 = 36\) and \(6 + 6 = 12\).

Step 3 ：Therefore, the factored form of the expression is \((m+6)(m+6)\) or equivalently, \((m+6)^{2}\).

Step 4 ：\(\boxed{(m+6)^{2}}\) is the final answer.