1. The problem asks to expand the expression $2\log_4(X+4)$.\n\n2. Recall the logarithm power rule: $a\log_b(c) = \log_b(c^a)$. This means we can rewrite the coefficient 2 as an exponent inside the logarithm.\n\n3. Applying the power rule: $$2\log_4(X+4) = \log_4\big((X+4)^2\big)$$\n\n4. The expanded form of the logarithm is therefore $\log_4\big((X+4)^2\big)$. This is the simplified expanded form using logarithm properties.\n\n5. If desired, you can expand the square inside the logarithm: $$(X+4)^2 = X^2 + 8X + 16$$\n\n6. So the expression can also be written as: $$\log_4(X^2 + 8X + 16)$$\n\nThis completes the expansion of the original expression.