What can you say about the end of behavior of the function f(x)=-4x^6+6x^2-52?

For end behavior, we need to consider 2 things: the highest exponent, and the coefficient of the highest exponent.
the highest exponent is 6, an even number, which means that the end behaviors will both be ∞ or -∞.
Since the coefficient is -4, a negative number, the end behaviors will both be -∞.
As x→ -∞, f(x)→ -∞. As x→ ∞, f(x)→ -∞.

Letter a i would say

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