ln 555.6/281.1 = -deltaH vap/8.314J/k mol [1/256.1K - 1/242K]. I have to solve for delta Hvap.

I know that the left side would be7.21. I am not sure what step to do next.

No, it isn't 7.21.

ln(555.6/281.1) = ln(1.976) = 0.681
0.681 = (x/8.314)(1/256.1 - 1/242).
I would evaluate the T terms first.
0.681 = (x/8.314)(-0.0002275)=
(0.681*8.314)/-0.0002275 = x = dHvap