When m takes what value, the solution of the equation 4x + m (X-6) = 2 (2 + 3M) about X is a positive integer Attention! It's 2 + 3M, not 2-3m

When m takes what value, the solution of the equation 4x + m (X-6) = 2 (2 + 3M) about X is a positive integer Attention! It's 2 + 3M, not 2-3m

4x+m(x-6)＝2(2+3m)
→x＝12-44/(m+4).
∵44＝11×4＝22×2＝44×1
Or 44 = (- 11) × (- 4) = (- 22) × (- 2) = (- 44) × (- 1)
So,
M + 4 = 4, that is, when m = 0, x = 1;
M + 4 = 44, that is, when m = 40, x = 11;
When m + 4 = 22, M = 18, x = 10;
When m + 4 = - 22, i.e. M = - 26, x = 14;
M + 4 = - 44, that is, when m = - 48, x = 13;
When m + 4 = - 1, i.e. M = - 5, x = 56;
When m + 4 = - 2, i.e. M = - 6, x = 34;
When m + 4 = - 4, i.e. M = - 8, x = 23
in summary,
When m = 0, 40, 18, - 8, - 26, - 48, - 5, - 6, - 8,
The solution of the original equation is a positive integer