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The presenter switches from numerical examples to an algebraic proof because checking specific cases like $6\times8=48$ and $2\times4=8$ only verifies the statement for those particular pairs. To prove the universal statement that the product of *any* two even numbers is even, a general algebraic argument is required to cover all possible even numbers.

Conditions: The goal is to prove a universal statement about all even numbers.; Numerical examples are used only to build intuition.; Algebra is necessary for a general proof.

The presenter switches from numerical examples to an algebraic proof because checking specific cases like $6\times8=48$ and $2\times4=8$ only verifies the statement for those particular pairs. To prove the universal statement that the product of *any* two even numbers is even, a general algebraic argument is required to cover all possible even numbers.

Conditions: The goal is to prove a universal statement about all even numbers.; Numerical examples are used only to build intuition.; Algebra is necessary for a general proof.