Answer
$-2062$
Work Step by Step
${}_{n}C_{r}=\displaystyle \frac{n!}{(n-r)!r!}$
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$\displaystyle \frac{46!}{44!}=\frac{46\times 45\times 44!}{44!}=46\times 45=2070$
${}_{10}C_{3}=\displaystyle \frac{10!}{(10-3)!3!}=\frac{10\times 9\times 8}{1\times 2\times 3}=120$
${}_{6}C_{4}=\displaystyle \frac{6!}{(6-4)!4!}=\frac{6\times 5}{1\times 2}=15$
$\displaystyle \frac{{}_{10}C_{3}}{{}_{6}C_{4}}=\frac{120}{15}=8$
$\displaystyle \frac{{}_{10}C_{3}}{{}_{6}C_{4}}-\frac{46!}{44!}= 8-2070=-2062$
