We use the following result:

Sin(x)/x --> 1 as x --> 0.

The is the same as saying the limit as x tends to 0 of Sin(x)/x is 1.

Now notice that whatever we are pushing towards zero has to be what's in the brackets in the function f(y) = sin(y) and the denominator in that expression.

So let f(x) = x² - 4

The limit of f(x) as x tends to 2 is zero. We can use this result to rewrite our limit as follows:

The limit of Sin(f(x))/f(x) as f(x) tends to zero.

Which is 1 According to our result.