In your situation, the LCD is (x - 4)(x + 2). If you're having trouble with LCDs in general, see this lesson:
Adding and Subtracting Rational Expressions
In general, you have to determine if the denominators have any common factors. For instance, the lowest common denominator in the example
is because the two fractions' denominators share the common factor of x + 3. If the denominators share no common factors, then the lowest common denominator is the product of each of the individual denominators.