The multiplication of 476 by 584 is

We have to evaluate the expression $476\times 584$.

Now, 476 multiplied by 4 is $476\times 4 =1904$.

Also, 476 multiplied by 80 is $476\times 80 =38080$.

Last, 476 multiplied by 500 is $476\times 500=238000$.

Adding all the three values, we get $1904+38080+238000 = 277984$.

So, the multiplication of 476 by 584 is 277984.

Hence, the correct answer is option C.