All rational zeros of a polynomial in descending order, 
if there are any, are fractions with a numerator which 
is ± an integer factor of the last term in absolute value,
and a denominator which is ± an integer factor of the first 
coefficient in absolute value.

The factors of the last term, 6, in absolute value are

1, 2, 3, 6 

The factors of the first coefficient, -4, in absolute value
are

1,2,4.

No we make all possible fractions which have a numerator 
of 1,2,3,or 6 and a denominator 1,2, or 4:

1/1, 1/2, 1/4, 2/1, 2/2. 2/4, 3/1, 3/2. 3/4, 6/1, 6/2, 6/4

Now we reduce them all

1, 1/2, 1/4, 2, 1. 1/2, 3, 3/2. 3/4, 6, 3, 3/2

Now we remove the duplications:

1, 1/2, 1/4, 2, 3, 3/2, 3/4, 6.

Now we put ± beside them all:

±1, ±1/2, ±1/4, ±2, ±3, ±3/2, ±3/4, ±6.

If there are any rational zeros, they are among
these 16.  

Edwin