How do i solve |2y-4|=12 and |3z|-4> 8

To solve absolute value equations you should split it up, one side keep it as it is and the other should negate the argument (the part in between the abs. value signs) 

For the first question, you should follow the steps above. 

2y-4=12
+4=+4
2y=16
divide by 2
y=8

-2y+4=-12
-4=-4
-2y=-16
divide by -2
y=-8

y={-8,8} should be your answer.

For the second question do the same if I'm not mistaken:

-3z+4>-8
-4=-4
-3z>-12
divide by -3 (remember to flip the sign when dividing or multiplying by a neg. number. 
z<4

3z-4>8
4=4
3z>12
z>4. 

The answer is 4<z>4 or (4,4)