To find the limit of the function lim sin^2(4x)/(6x^2) as x approaches 0, we can simplify the expression.

First, we know that sin(0) = 0, so sin(4x) is approximately 4x when x is close to 0.

Therefore, sin^2(4x) is approximately (4x)^2 = 16x^2.

Now, our expression becomes:

lim (16x^2)/(6x^2)
x->0

Simplifying further, we get:

lim 16/6
x->0

Therefore, the limit of the function is 16/6 = 8/3 as x approaches 0.