The Law of Syllogism is valid argument of deductive reasoning, it's like the transitive property of inqualities, if a = b and b = c then a = c. The important thing here is to create new statement following the given conditional.
The first statement is: if 2x = 6, then x = 3.
A new conditional statement would be: if 2x = 6, then x = 6/2.
The second statement is: if 4x = 12, then 2x = 6.
A new conditional statement would be: if 4x = 12, then x = 3.
The third statement is: if x = 3, then x = 3.
A new conditional statement would be: if x = 3, then 3 = x.
The fourth statement is: if x = 3, then 4x = 12.
A new conditional statement would be: if x = 3, then 2x = 6.