There are many methods to solve this kind of equations.
You could multiply the top one by 3 and the bottom one by 2:
3 * (3x+2y) = 3*(4)
2* (4x+3y) = 2*(7)
Which gives us:
9x+6y=12
8x+6y =14
We subtract the bottom one from the top one:
(9x-8x)+(6y-6y) = (12-14)
x = -2
Since we know the value of x that satisfies the equation, we just need to substitute it in any of the starting ones:
3*(-2)+2y=4
2y = 10
y = 5
You can verify if you got the correct answer by substituting the values you find in both equations you started with.
