$[x^{50}](x^{6} + x^{7} + x^{8} + ...)^{6}$
$[x^{50}](x^{6}(1 + x^{2} + x^{3} + ... ))^{6}$
$[x^{50}](x^{36})(1 + x^{2} + x^{3} + ... )^{6}$
$[x^{14}](1 + x^{2} + x^{3} + ... )^{6}$
$[x^{14}](\frac{1}{1-x})^{6}$
$[x^{14}](1-x)^{-6}$
$[x^{14}]\binom{-6}{14}(-1)^{14}$
$[x^{14}]\binom{14 + 6 - 1}{14}(-1)^{14}(-1)^{14}$
$[x^{14}]\binom{19}{14}$
$[x^{14}]\binom{19}{5}$
$\binom{19}{5}$ is the answer
Refer https://youtu.be/ZyUb5UxBA9Q