I am going to spell out each property along the way.
x/2 = 2
Multiply both sides by 2. The Multiplication Property of Equality allows us to multiply both sides by the same number. The Multiplication Property of Equality says if a = b, then a·c = b·c. In this case, a is x/2 and b is the 2 on the right hand side of the equal sign. Let c also be 2.
a·c = b·c
(x/2)·2 = 2·2
(x/2)·2 = 4
Now, we want to cancel out the 2's on the left. First, we need to reorder the left side.
2·(x/2) = 4
This reordering can be done by the commutative property of multiplication (a·b = b·a).
The associative property of multiplication allows us to do the multiplication between 2 and x first. The associative property states a(b·c) = (a·b)c
2·x/2 = 4
The commutative property of multiplication then allows:
x·2/2 = 4
The inverse property of multiplication states a·1/a = 1. The inverse property of multiplication then allows:
x·1 = 4
The identity property of multiplication states a·1 = a. The identity property of multiplication then allows:
x = 4.
Now, personally, I find this kind of work very tedious. But being able to work stepwise through a problem using one property at a time is a useful skill for higher math courses such as geometry and linear algebra. Most of the time though, we just use these properties without remembering why we can use them or what they are called.