The answer to $\lim _{x \rightarrow 0} \frac{\sin (4 x)}{x}$ is

Step 1 ：The given limit is of the form $\lim _{x \rightarrow 0} \frac{\sin (4 x)}{x}$

Step 2 ：The limit of the form $\frac{sin(x)}{x}$ as $x$ approaches 0 is 1

Step 3 ：We have a similar form but with $4x$ instead of $x$

Step 4 ：We can use the property of limits that says the limit of a function times a constant is the constant times the limit of the function

Step 5 ：So, we can take the 4 out of the sine function and multiply it with the limit

Step 6 ：The limit then becomes $4 \times \lim _{x \rightarrow 0} \frac{\sin (x)}{x}$

Step 7 ：Substituting the limit value, we get $4 \times 1$

Step 8 ：Final Answer: The answer to $\lim _{x \rightarrow 0} \frac{\sin (4 x)}{x}$ is \(\boxed{4}\)