How do you write two different addition equations that have $12$ as the solution?

Hint: In the question, a statement is given to find out the equations. So we need to know the format of the resultant equation. After writing the equation format we need to substitute the certain value for a certain term in the equation.

Complete step-by-step answer:
To solve the question first we need to limit the equation to the linear by using the integer coefficients of the form
Now the equation is
\[\Rightarrow ax+b=c\left\{ a,b,c\in \mathbb{Z} \right\}\]
As in the question, there is an infinite number, so the above equation limiting restriction is not compulsory in answer to solve the question.
Here we need to find the two separate and different equations which are in the format of $ax+b=c$ where $x=12$
To simplify the equation, let’s assume
$a=1$
As we assumed the value of an as one so, we will have possible equations in infinite numbers.
Now we get the equation after substituting the value of an as
$\therefore x+b=c$
Here we need to make the value of $x=12$
So the equation changes as
$\Rightarrow c-b=12$
$\Rightarrow c=b+12$
By keeping the b value as any number $\in \mathbb{Z}$
Now, for the value
$b=-1$

$\begin{align}
  & \Rightarrow c=11 \\
 & \Rightarrow x-1=11 \\
\end{align}$
Is the first example
Now, for the value
$b=-2$
$\begin{align}
  & \Rightarrow c=10 \\
 & \Rightarrow x-2=10 \\
\end{align}$
And the example can be calculated so on.
So there are so many equations that satisfy the statement in the question.

Note: Generally the linear equations are in two variables. In the linear equations, there are many types and they can be solved in three patterns. Inconsistent, independent, and dependent are the types of linear systems. We can also write another two equations as x + 4 = 16 and x + 2 = 14.