If the number of terms in the expansion of 1 - 2 x + 4 y 2 n ,   x ,   y ≠ 0 , is 28 , then…

${\left(1-\frac{2}{x}+\frac{4}{y^2}\right)}^n$

We know, if having three variables then total number of terms would be $\frac{\left(\mathrm{n}+1\right)\left(\mathrm{n}+2\right)}{2}$

$\Rightarrow \frac{\left(\mathrm{n}+1\right)\left(\mathrm{n}+2\right)}{2}=28$

$\therefore \left(\mathrm{n}+1\right)\left(\mathrm{n}+2\mathrm{ }\right)=56$

Which gives $\mathrm{n}=6$ , and sum of coefficients would be 

${\left(1-2+4\right)}^6=3^6=729$ .