The sequence is: 4, 196, 16, 144, 36, 100, 64, X.

Notice that the numbers alternate between small and large values: 4, 16, 36, 64: These are squares of 2, 4, 6, and 8 (i.e., $2^2$, $4^2$, $6^2$, $8^2$). 196, 144, 100: These are squares of 14, 12, and 10 (i.e., $14^2$, $12^2$, $10^2$).

The pattern is: The small numbers follow the squares of even numbers: 2, 4, 6, 8. The large numbers follow the squares of even numbers in reverse: 14, 12, 10. For the next large number:

After 14, 12, 10, the next number should be 8. The square of 8 is 64. Thus, X = 64.