Question 4827
Any problem with word "consecutive integers" should make you think about:

x, x+1, x+2, ...

Any problem with word "consecutive even integers" should make you think about:

x, x+2, x+4, ...

x is the first number, and x+2, x+4, etc are next consecutive even number.

Next, you translate English into Algebrese:

first: x
second: x+2
twice the sum of the first and second: 2*(x+(x+2))
three times the third: 3*(x+4)
10 more: 10+

2*(x+(x+2)) = 10 + 3*(x+4)

2x+2x+4 = 10 + 3x + 12
2x+2x-3x = 10 + 12 - 4
x = 18

please double check that my solution is correct.