You have the following intersection:
(-2 < 2x - 6) ∩ (3x - 12 ≤ 10)
The intersection of the previous inequalitues gives a unique interval result. To calculate such an interval you first solve each of the implied inequalities:
-2 < 2x - 6 sum 6 both sides
-2 + 6 < 2x - 6 + 6
4 < 2x divide by 2 both sides
4/2 < 2x/2
2 < x
x > 2
3x - 12 ≤ 10 sum 12 both sides
3x - 12 + 12 ≤ 10 + 12
3x ≤ 22 divide by 3 both sides
x ≤ 22/3
x ≤ 7.333...
Then, you have that x>2 and also x≤7.333...
Hence, the solution of the intersection to both inequalities is:
x/x ∈ (2 , 22/3]
The upper limit is a closed parenthesis because of the lower or equal symbol.