In the given figure, BAC is a right angle, which means that angle B is a right angle as well. Using the Pythagorean theorem, we can determine the length of BC: BC^2 = AC^2 - AB^2. Substituting the given values, BC^2 = 6^2 - 2^2 = 36 - 4 = 32.

To find the length of BE, we need to determine the length of BA. Since angle B is a right angle, triangle BAE is also a right triangle. Using the Pythagorean theorem, we can find the length of BA: BA^2 = EA^2 + BE^2. Substituting the known values, BA^2 = 2^2 + BE^2 = 4 + BE^2.

Now, we can equate the expressions for BC^2 and BA^2: 32 = BA^2. Since we know that BA^2 = 4 + BE^2, we can solve for BE: 32 = 4 + BE^2. Subtracting 4 from both sides, we get 28 = BE^2. Taking the square root of both sides, we find that BE = √28