As x gets larger the constants become insignificant so the expression becomes:
(4x3-3x2)/(6x3+4x)=(4x2-3x)/(6x2+4). Again, the constant becomes negligible:
(4x2-3x)/6x2=(4x-3)/6x. Dropping the constant again: 4x/6x=⅔, which is the limit as x→∞.
Actually, we can ignore all but the highest degree of x and we get the same result.