$$ \begin{split} &2^{1 + x} &\cdot 3^x \\ = & 2^1 \cdot 2^x &\cdot 3^x \\ = & 2^1 &\cdot 6^x \\ = & 2 &\cdot 6^x \end{split} $$

$$ \begin{split} & 4^{2x} : 2^x \\ = &(4^2)^x : 2^x \\ = &16^x : 2^x \\ = & \left( \frac{16}{2} \right) ^x \\ = & 8^x \end{split} $$