If a7! + b8! + c9! + d10! = x, where a, b, c and d are natural numbers that are not multiples of 10, then how many distinct values of unit’s digit of x are possible?

it could be written as 7!(a+8b+72c+720d) so the expression is a multiple of 7!..... since 7!=5040 any multiple of 7! will have 0 as units digit therefore only one value of units digit is possible