The number of factors of 1800 that are multiple of 6 is:

There are 18 factors of 1800 that are multiples of 6. The factorisation $1800=2^3\cdot3^2\cdot5^2$ gives three choices for the positive exponent of 2, two for the positive exponent of 3, and three for the exponent of 5. Multiplying gives $3\times2\times3=18$, while 27 includes the factors with no 3.