There is already a solution here but in that solution they write under step 2/2:

Substituting the values from the image, we get:

Probability of Up = (1.2 - 1.05) / (1.1 - 1.05) = 0.75 but that is not true since the answer there is 3. Could someone provide me with the steps to this question from start to finish?

18. You are in a two-period world where a risk-free and risky asset are traded, see the figure below for the prices and payoffs. You have a project that costs 7 at time zero and pays 8 in the up and then up state, 9 in the up and then down state, 10 in the down and then up state, and 11 in the down and then down state. What is the NPV of this project