From the first equation,
2X+3Y= -6
2X = -6 - 3Y
X = -(6 + 3Y)/2
So replace X value in the second equation,
4X - Y = 16
4(-(6+3Y)/2) - Y = 16
-12 - 7Y = 16
-7Y = 28
So Y= -4
Then We can find the X value from first or second equation,
2X + 3Y = -6
2X + 3x(-4) = -6
2X -12 = -6
2X = 6
X = 3