First order equation with one unknown variable 
Problem Given: Twelve years ago the age of $A$ was the double of age of $B$ and in the next twelve years, the age of $A$ would be $68$ years less than triple of $B$. Find the current ages.

What I've done is set up the equations
$$2x-12=3(x+12)-68+12$$ 
where $2x-12$ is the age of $A$, $3(x+12)$ is the triple of age of $B$ in the future $(+12)$. And the last $12$ because in the sentence says 'is in the next twelve years.'
But the answer doesn't match with the solution on the book $A=52$ and $B=32$.
Could someone tell how to solve?
 A: Twelve years ago the age of A was the double of age of B so .........$$A-12 = 2(B - 12)$$
$$2B - A = 12 \tag{1}$$
In the next twelve years, the age of A would be 68 years less than triple of B so ......$$3(B + 12) - (A + 12) = 68$$
$$3B - A = 44 \tag{2}$$
Subtract $(1)$ from $(2)$:
$$B = 32$$
Then $$A = 52$$
A: Since for some reason no one felt the need to elaborate on where these equations came from, much less OP's error, I'll do it then. 
Though a word of import -- To note for future reference, OP, showing your process might help because otherwise no one can really understand where your own errors come from without it. I happened on your error by simply working the problem the same by mere coincidence; these problems can be solved many different ways, so it's merely luck we coincided.
I'm going to start from the beginning.


Twelve years ago the age of A was the double of age of B and in the next twelve years, the age of A would be 68 years less than triple of B. Find the current ages.

Let $A,B$ denote the respective persons' ages. Then, since "Twelve years ago the age of A was the double of age of B," we know
$$A - 12 =2(B - 12) = 2B - 24 $$
Similarly, per "in the next twelve years, the age of A would be 68 years less than triple of B," we know
$$A + 12 = 3(B+12) - 68 = 3B + 36 - 68 = 3B - 32$$
This gives us a system of equations:
$$A - 12 = 2B - 24$$
$$A + 12 = 3B - 32$$
Equivalently, since $A$ seems easiest to solve for,
$$A = 2B - 12 = 3B - 44$$
Thus, we have the equation in $B$, for which we solve:
$$2B - 12 = 3B - 44 \;\;\; \Rightarrow \;\;\; B = 32$$
Plug $B = 32$ into any equation of our system of equations, and you'll find $A = 52$.

As for where your error lies, OP, it's this:

What I've done is
  $$2x-12=3(x+12)-68+12$$ where
  $2x-12$ is the age of $A$, $3(x+12)$ is the triple of age of $B$ in the future $(+12)$. And the last $12$ because in the sentence says 'is in the next twelve years.'

That last $+12$ is unnecessary. Yes, it is in $12$ years from the present, but that $12$ years is meant to turn $x$ into $x+12$ (as you already have done in parentheses). Since, at that $12$-year-mark, the "$68$ less than the triple" relation is satisfied, you do not add a further $12$.
A: The problem with your attempted solution is you are using one unknown $x$ for two people. You must use two unknowns for two people.  
You can organize all in table:
$$\begin{array}{c|c|c}
&12 \ \text{years ago}&Now& 12 \ \text{year after}\\
\hline
Adam&A-12&A&A+12\\
Beth&B-12&B&B+12\\
\hline
Conditions&A-12=2(B-12)&&A+12=3(B+12)-68\end{array}.$$
Can you solve the system of two equations and find $A$ and $B$? 
