$\text{ The sum of the coefficient of }(x+y{)}^n\text{ is }64,\text{ then greatest coefficient is }$

$\text{ The sum of the coefficient of }(x+y{)}^n\text{ is }64$

$\Rightarrow 2^n=64=2^6$

$\Rightarrow n = 6$

$\therefore \text{ Greatest coefficient is }{}^{n}C_{\frac{n}{2}}=6_{C_3}=20$