since both equations are equal to y...
y = 2x + 10
y = -4x - 2
2x + 10 = y = -4x - 2
2x + 10 = -4x - 2
2x + (4x) = -2 + (-10)
6x = -12
x = -2
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plug in x = -2 into one of those equations: I will use y = 2x + 10
y = 2(-2) + 10
y = -4 + 10
y = 6
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okay, so I rechecked my answers several times, and I still got (-2,6)
That MC question has an error since none of the answer choices fit.
Inform your teacher about this.
(I'd say choose that (-3,4) since it works only for one equation y = 2x +10 .... maybe your teacher was supposed to use the other equation instead of y = -4x - 2)