f(1)=1-3+4-6+4=0 so x=1 is a zero. Also f(2)=16-24+16-12+4=0 so x=2 is another zero.
Using synthetic division let's divide by the zero x=1:
1 | 1 -3 4 -6 4
1 1 -2 2 | -4
1 -2 2 -4 | 0 = x3-2x2+2x-4. Since 1-2+2-4 is not zero, x=1 is not another zero.
Nor is x=-1, since -1-2-2-4 is not zero. Let's try x=2: 8-8+4-4=0 so x=2 is a zero, and we can divide by this:
2 | 1 -2 2 -4
1 2 0 | 4
1 0 2 | 0 = x2+2, which has complex zeroes: -i√2 and i√2.
The zeroes are 1, 2, -i√2 and i√2.