To find the total effect on their checking account balance from the deductions made for childcare, we can multiply the monthly deduction by the number of months in a year.
The Walkers deducted $850 each month for 12 months:
\[ 850 , \text{(monthly deduction)} \times 12 , \text{(months)} = 10,200 \]
Since this amount is deducted from their checking account, the effect on their checking account balance would be a decrease of $10,200.
So, the correct response is:
-$10,200