To calculate x and y, we'll group, both sides, the real parts and the imaginary parts.

First, we'll move the terms in x and y, to the left side.

-4x + 3iy = -2 + 6i

To the left side, the real part is -4x and the imaginary part is 3y.

We'll put the real part from the left side equal to the real part from the right side:

-4x = -2

We'll divide by -4:

**x = 1/2**

We'll put the imaginary part from the left side equal to the imaginary part from the right side:

3y = 6

We'll divide by 3:

**y = 2**

2+3yi = 4x+6i

Solution:

Since 2+3yi = 4x+6i

The real parts on both sides are equal . The maginary parts on both sides are equal.

2 = 4x..........(1)

3y = 6...........(2)

The 1st equation gives x = 2/4 = 1/2

The 2nd equation gives y = 6/3 = 2.

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