Find the value of $2\left(\frac{7!}{3!4!}\right)$
We can simplify directly

\begin{align*}
2\left(\frac{7!}{3!4!}\right) &= 2\left(\frac{7\cdot 6 \cdot 5}{3 \cdot 2 \cdot 1}\right) \\
&= \frac{7 \cdot 6 \cdot 5}{3 \cdot 1} \\
&= 7 \cdot 2 \cdot 5 \\
&= \boxed{70}
\end{align*}