Let's start with first equation

We need to bring both equations in the form y = mx + b

2x + 3y = 7            (original equation)

-2x          -2x           (subtract 2x from both sides)

________________

3y = -2x + 7

(3y/3) = (-2x + 7)/3         (divide both sides by 3)

y = (-2/3)x + 7/3 --------------(1)

Let's do the second equation

4x + 6y = 11                 (original equation)

-4x          -4x                 (subtract 4x from both sides)

____________

6y = -4x + 11

(6y/6) = (-4x + 11)/6     (divide both sides by 6)

y = (-4/6)x + 11/6

or y = (-2/3)x + 11/6     --------------------(2)

As, you can see slopes in both equations (1) and (2) are same. That's why these lines are parallel.