set the integers equal to x, x+1, x+2, x+3, x+4, x+5, x+6

sum of all integers = 7x+21

21*4 = 84

7x + 21 = 84(x+6)

7x + 21 = 84x + 504

-483 = 77x

x is not an integer, thus there is no solution. However, as I interpreted * to signal multiplication, but the word "times" is written out immediately afterwards, I believe the question is incorrectly formatted.