Let's solve each equation separately:

1)

(x + 4y)/9 - (x - 2y)/3 = 0
(x + 4y)/9 - (x - 2y)/3 = (3(x + 4y) - 9(x - 2y))/27
(x + 4y)/9 - (x - 2y)/3 = (3x + 12y - 9x + 18y)/27
(x + 4y)/9 - (x - 2y)/3 = (-6x + 30y)/27
(-6x + 30y)/27 = 0
-6x + 30y = 0
-6x = -30y
x = 5y

Therefore, the solution to the first equation is x = 5y.

2)

(x + 2y)/10 - (x + 4y)/8 + 10 = (2x - 3y)/2 - (x + y)/6
(x + 2y)/10 - (x + 4y)/8 + 10 = (2x - 3y)/2 - (x + y)/6
(4(x + 2y) - 5(x + 4y) + 80)/40 = (12x - 18y - 4x - 4y)/12
(4x + 8y - 5x - 20y + 80)/40 = (8x - 22y)/12
(-x - 12y + 80)/40 = (8x - 22y)/12
(-x - 12y + 80)/40 = (24x - 66y)/36
(36x + 432y - 2880)/1440 = (1440x - 3960y)/1296
1296(36x + 432y - 2880) = 1440(1440x - 3960y)
467856x + 563904y - 3732480 = 2073600x - 5702400y
467856x + 563904y - 2073600x + 5702400y = 3732480
-1605744x + 6266304y = 3732480
-401436x + 1566576y = 933120

Therefore, the solution to the second equation is -401436x + 1566576y = 933120.