Multiply each side of the equation by 3: b-9=3b+27; subtract 27 from each side: b-36=3b, or 3b=b-36. Subtract b from each side: 2b=-36; divide both sides by 2: b=-18. We could have subtracted b from each side first then subtracted 27, giving us -36=2b; halve both sides: -18=b, which is the same as b=-18. The important thing is to get the unknowns (letters) on one side and the knowns (numbers) on the other side of the equals.
CHECK
Put b=-18 into the original equation: (1/3)(-18-9)=(1/3)(-27)=-9; b+9 is -18+9=-9, so the equation is true. Therefore b=-18.