@epsilontik, I assume that you mean that just 6 positive reals are given (corresponding to the distances between certain 4 points of the Euclidean plane.

The answer is NO--such data cannot determine the convexity because the same 6 positive reals can stand for two completely different 4-point sets, where in one case none of the points belongs to the convex hall of the remaning three, while in the other case one will. After connecting these points, in each case separately, by straight intervals, the (non-intersecting) diagonals in the non-convex case will have lengths equal to the lengths of two of the sides in the other case.