We can simplify the expression by first rewriting each of the bases as powers of 2:
$$8^{n} \times 2^{2n} \div 4^{3n} = (2^{3})^{n} \times 2^{2n} \div (2^{2})^{3n}.$$
Using the laws of exponents, we can simplify this to:
$$(2^{3n}) \times 2^{2n} \div 2^{6n} = 2^{3n+2n-6n} = 2^{-n}.$$
Therefore, the simplified expression is \(2^{-n}\).