Amir's checking account charges a $9.75 monthly service fee and a $0.12 per-check fee. if amir writes 15 checks per month, should he switch to a checking account that charges an $11.50 monthly service fee and no per-check fee

Amir should switch because his monthly fee are currently greater than $11.50. So, if each check costs $0.12 cents, and he writes 15 a month, you multiply 0.12 by 15
0.12 times 15 equals $1.80
Additionally, you add $1.80 to $9.75, which comes out to $11.55
In summary, you will spend 5 cents more on the fist plan, than you would on the second.
thats why you should switch.