A total of 4 + 6 = <<4+6=10>>10 cars are in the shop throughout the week.
This means the shop buys 10 cars * 4 tires = <<10*4=40>>40 tires.
For each of the customers that only want half the tires changing, there are 4 tires * 0.5 = <<4*0.5=2>>2 tires left over.
Two of the customers only want half the tires changing, so there are 2 tires * 2 cars = <<2*2=4>>4 tires left over from these customers.
Out of the remaining tires, there are 20 – 4 = <<20-4=16>>16 tires left from customers who don't want their tires changing.
So in total, there were 16 tires / 4 tires per customer = <<16/4=4>>4 customers who did not want their tires changing.
#### 4