She worked as a carpenter for 12 hours and as a blacksmith for 18 hours.
Assuming you mean she earned $20 as a carpenter and $25 as a blacksmith per hour, with a total of 30 hours for $690,
let c represent carpenter hours and b for blacksmith hours.
20c + 25b = 690
c + b = 30
Subtract b from each side so that c = 30 - b
Plug this value into the first equation
20(30 - b) + 25b = 690
600 - 20b + 25b = 690
600 + 5b = 690
5b = 90
b = 18
To find c, plug this value of b into the other equation
c + 18 = 30
c = 12
Your friend is incorrect.
You should always count 0's when deciding where to place the decimal point. To disprove your friend, you could divide 1.2 by 8 and see that it doesnt equal 1.5. Also, 8 is multiplied by a value that is more than one, so the result should be higher than 8.
Good luck with your assignment!