The y-intercept represents the initial girth of the tree. Assuming that the X-axis represents time in this scenario (as it usually does) the y-axis, therefore, represents the girth of the tree. The y-intercept is located where X = 0. So if no time has passed then this must be the first measurement of the girth of the tree.
The surface area is the sum of the are of all sides. One side's area is 64 in^2 and since it's a cube, all sides will be the same. 64*6 = 384 The surface area is 384 in^2