Just 4 x 2/3 x cos(0.75 rads)

Remember, the dot product is a scalar and invariant under rotation and reflection transformations. This means you can draw any two vectors that fit the description, and they should all give you the same answer.

E.g. First vector has length 4 along x-axis. Second vector has length 2/3 rotated 0.75 rads on the x-y plane. Now you can obtain the same result analytically.