Math is sometimes very much like learning another language. You have to "translate" the words into a math equation.
You can pick any letter to stand for an unknown number, but most often we use n or x.
So, starting at the beginning of your question, we have:
"three added to a number" n + 3
"this sum is doubled" (n + 3) times 2
We usually write it with the single digit first 2(n+3)
"the result" is our 2(n + 3)
"2 more than the number" n + 2
So, 2(n + 3) = n + 2
There is your equation. To solve it, you have to use the distributive property to multiply 2 by both terms in the parentheses:
2 * n + 2 * 3 = n + 2 which is:
2n + 6 = n + 2
You have the variable on both sides of the equation, so you subtract it from both sides (remember that you have to do the same thing to both sides of the equation to keep it in balance).
2n - n + 6 = n - n + 2
2n - n is really 2n - 1n, so the left side of the equation is 1n + 6 (and we can write is as without the 1); on the right side, the n - n cancels out.
n + 6 = 2
We then subtract 6 from both sides:
n + 6 - 6 = 2 - 6 and we get:
n = -4
You can now read the original sentence and plug -4 in:
3 + -4 = -1; doubled is -2; the result is 2 more than -4. -2 is 2 more than -4, so it works. :-)
Hope this helps!