To solve this problem, we need to determine the number of triangles that can be formed using the given conditions. Let's break it down step by step.

1. Analyzing the sides:
- We have a convex quadrilateral ABCD with sides AB, BC, CD, and DA.
- We need to count the number of triangles with vertices on different sides. This means that the vertices of the triangles cannot be collinear.

2. Considering the points on the sides:
- We are given that 3 points are marked on side AB, 4 points on side BC, 5 points on side CD, and 6 points on side DA.
- Let's assume the points on side AB are A1, A2, A3. Similarly, the points on sides BC, CD, and DA are B1, B2, B3, C1, C2, C3, D1, D2, D3 respectively.

3. Counting the number of triangles:
- To form a triangle, we need to select 3 points out of the given points.
- On side AB, we have 3 points, so we can select 3 points in C(3,3) = 1 way.
- Similarly, on side BC, we have 4 points, so we can select 3 points in C(4,3) = 4 ways.
- On side CD, we have 5 points, so we can select 3 points in C(5,3) = 10 ways.
- On side DA, we have 6 points, so we can select 3 points in C(6,3) = 20 ways.

4. Calculating the total number of triangles:
- To calculate the total number of triangles, we need to multiply the number of ways to select points on each side.
- Total number of triangles = 1 x 4 x 10 x 20 = 800.

5. Considering restrictions:
- However, we have to consider the restriction that the vertices of the triangles cannot be collinear.
- If any three points are collinear, they cannot form a triangle.
- As the number of collinear points is not given, we cannot determine the exact number of triangles that can be formed.

Therefore, the correct answer is option 'D' - none of these, as we cannot determine the number of triangles with the given information.