Inverted nine

In the hotel,, Inverted nine" each hotel room number is divisible by 6. How many rooms we can count with three-digit number registered by digits 1,8,7,4,9?

Correct result:

n =  18

Solution:

n1=114 n2=714 n3=414 n4=174 n5=774 n6=474 n7=894 n8=144 n9=744 n10=444 n11=984 n12=918 n13=978 n14=198 n15=798 n16=498 n17=948 n18=888 n=18

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