Rational zeroes are ±1, ±2, ±4, ±8 (factors of 8). To find the actual zeroes we can use synthetic division.
Example:
1 | 1 6 7 -6 -8
1 1 7 14 8
1 7 14 8 so 1 is a zero (root).
Without going into details (for convenience), the same process can be used with all other potential zeroes. When this done, the following the zeroes emerge -4, -2, -1, 1 so f(x)=(x-1)(x+1)(x+2)(x+4).