here balance means remainder

in order to solve we know that it should be a perfect multiple of 7 (As the remainder is 0). also we can see that it should end wither with 4 or 9 (since remainder is 4 when divided by 5), we can further remove 4 since remainder should be 1 when divided by 2 (it should be odd number).

now lets list multiples of 7 ending with 9

49 (7×7), 119(17×7), 189(27×7), 259(37×7)

49 is ruled out since remainder is 1 when divided by 8

if you see 119 it satisfied all the condition
119%8 -> 7
119%6 -> 5
119%4 -> 3
119%3 -> 2