To solve this problem, we need to consider the conditions given and find the maximum number of students who can see exactly four specific towers but not the other two. Here's the problem breakdown:

1. Six Towers (A, B, C, D, E, F): Each student can see towers at positions $A, B, C, D$ but cannot see towers $E$ and $F$.
2. Conditions:
   • The positions of the students and the towers are considered as points on the same plane, and these points are distinct and non-collinear.
   • No three towers lie on the same straight line.
   • A student cannot see a tower if it is blocked by another tower on the line of sight.

We need to determine the maximum number of students satisfying these conditions.

Solution Steps:

1. Visualize the Problem:

   • Imagine the plane with the six towers labeled $A, B, C, D, E,$ and $F$.
   • Position the students such that they can only see towers $A, B, C,$ and $D$.

2. Blocking Condition:

   • The key is understanding the blocking condition. For instance, if a student is at a position $P$ and the line $PA$ intersects $PB$, the view to $B$ might be blocked.

3. Non-Collinear Condition:

   • The towers $A, B, C, D, E, F$ should be placed such that no three are collinear.

4. Strategic Positioning:

   • Place towers $A, B, C,$ and $D$ in such a way that from any given student's position $P$, the lines to $E$ and $F$ are always blocked by one of $A, B, C,$ or $D$.

Given these steps, the problem transforms into a geometric arrangement problem where we strategically place students and towers.

From geometric configuration, we can position students such that each student’s view of towers $A, B, C,$ and $D$ is not blocked by any other student while ensuring $E$ and $F$ are blocked.

The maximum number of students will be determined by the strategic placement where each student can only see towers $A, B, C,$ and $D$.

Conclusion:

• With proper geometric placement, the maximum number of students is determined by how we can strategically place them in such a way that no line of sight to towers $E$ and $F$ remains unobstructed. Given no collinear points and six towers, the configuration should ensure each student's line of sight to towers $E$ and $F$ is blocked by one of the towers $A, B, C, D$.

Since no exact algorithm is provided, the problem can be solved optimally by trial and geometric configurations to ensure each student sees only the four towers but not the other two.

Ask for Further Clarification: Would you like a detailed geometric configuration for the positioning of towers and students to visualize the solution?

Here are five questions for further exploration:

1. How do we place students in a plane to see only specific towers?
2. What geometric principles can be applied to block the line of sight effectively?
3. Can the problem be modeled using combinatorial geometry?
4. How does non-collinearity affect the maximum number of students?
5. What are other potential solutions to ensure the blocking condition is met?

Tip: When solving geometric problems, visualize and sketch the configurations to understand blocking and line-of-sight constraints effectively.