Multiply. Assume all expressions are defined. $$ \begin{array}{l}\frac{4 x+16}{2 x+6} \cdot \frac{x^{2}+2 x-3}{x+4} \ 2(x-1) \ 4(x-1) \ 8(x-1) \ 4(x+1)\end{array} $$

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We start with the product
$$
\frac{4x+16}{2x+6} \cdot \frac{x^2+2x-3}{x+4} \cdot 2(x-1) \cdot 4(x-1) \cdot 8(x-1) \cdot 4(x+1).
$$

**Step 1.** Factor the expressions in the first two fractions.

Write the numerator and denominator of the first fraction in factored form:
$$
\frac{4x+16}{2x+6} = \frac{4(x+4)}{2(x+3)} = \frac{2(x+4)}{x+3}.
$$

For the second fraction, factor the quadratic:
$$
x^2+2x-3 = (x+3)(x-1),
$$
so that
$$
\frac{x^2+2x-3}{x+4} = \frac{(x+3)(x-1)}{x+4}.
$$

**Step 2.** Multiply the two fractions from the first line.
$$
\frac{2(x+4)}{x+3} \cdot \frac{(x+3)(x-1)}{x+4}.
$$
Cancel the common factors $$(x+4)$$ and $$(x+3)$$ (assuming these are nonzero):
$$
= 2(x-1).
$$

Now the product so far (including the factors from the remaining lines) becomes:
$$
2(x-1) \cdot 2(x-1) \cdot 4(x-1) \cdot 8(x-1) \cdot 4(x+1).
$$

**Step 3.** Multiply the coefficients and the binomials separately.

Multiply the numerical coefficients:
$$
2 \cdot 2 \cdot 4 \cdot 8 \cdot 4 = 512.
$$

For the binomials, notice that $$(x-1)$$ appears in the first four factors:
$$
(x-1) \cdot (x-1) \cdot (x-1) \cdot (x-1) = (x-1)^4,
$$
and there is an extra factor $$(x+1)$$.

**Step 4.** Write the final answer in factored form.
$$
512(x-1)^4(x+1).
$$
The final expression is $$512(x-1)^4(x+1)$$.

Multiply. Assume all expressions are defined. \( \begin{array}{l}\frac{4 x+16}{2 x+6} \cdot \frac{x^{2}+2 x-3}{x+4} \\ 2(x-1) \\ 4(x-1) \\ 8(x-1) \\ 4(x+1)\end{array} \)

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