Question

is the coordinate (-2, -4) a solution to the equation y=3x-2

Answer 1

$-4=3\cdot(-2)-2\\ -4=-6-2\\ -4=-8$

No.

Answer 2

Test:    (x, y)  = (-2, -4):

y = 3x -2

-4  =  3(-2) -2

-4 =   -6 -2

-4 = -8.  This is not true.  Therefore (-2, -4) is not a solution.