First, simplify each inequality.
Inequality 1: 4m - 2 < 8
Add 2 to both sides: 4m < 10
Divide both sides by 4 to isolate the variable: m < 5/2
Inequality 2: 6m +2 > 10
Subtract 2 from both sides: 6m > 8
Divide both sides by 6 to isolate the variable: m > 4/3
Now, graph these points on a number line. Note that each sign does not have the little line underneath it, and read as "less than" and "greater than". This means they are non-inclusive and each end point on the number line should be graphed as an open circle.