Question 654844
I suggest you look at other consecutive interger problem solved by DrBeeee. 
They are straight forward.
1. Let n = the smaller integer, then the next even integer is 
equal to n+2. Make sense? For example if the first intger is 18 the next one is 20 or 18+2.
Your first problem states that
(1) n = 10 + (n+2)/2, agree? 
All we need to do is simplify (1),
Multiply both sides by 2 (I hate fractions) to get
(2) 2*n = 20 + n + 2  or
(3) n = 22
Then the next number is 24. Right? How do we know? Check with (1).
Is (22 = 10 + (22+2)/2)?
Is (22 = 10 + 24/2)?
Is (22 = 10 + 12)?
Is (22 = 22)? Yes
Answer: The two consecutive even integers are 22 and 24. 
Note that we don't have to worry about whether or not n is even or odd, the problem statement satisfies that condition.
Let's do your next problem.
2. This statement is
(2) n + 2 = 3*n - 6 
Simplify and solve (2) for n,
(3) 2 + 6 = 3n - n or
(4) 2n = 8 or
(5) n = 4, then the next even integer is 6
Let's check with (2).
Is (4 + 2 = 3*4 - 6)?
Is (6 = 12 - 6)?
Is (6 = 6)? Yes
Answer: The two consecutive even integers are 4 and 6

I think you get it. Good luck with 3. and 4.
I can't help you on 3. because we don't know how any times etc. The answer to 4. is 6,8,10,12.