ANSWER
42.107
Step-by-step explanation
To round a number to the nearest thousandth we have to look at the next number. If that number is 5 or greater than 5, then we have to add 1 to the thousandths. If it's less than 5, then we leave it like it is and eliminate the other decimals.
In this case, the next number to the thousandth is 9, which is greater than 5. Therefore, we have to turn the 6 into a 7: 42.107