Find the value of x? - 4 - 7 - 6 - 5

I'd go with your third option, 6.

Half the diameter (the radius, also the hypotenuse for the right triangle) is 10 units. 

Half of the chord given by that blue line segment is 8 units. Now we do the Pythagorean Theorem (a² + b² = c²) to find the length of x.

x² + 8² = 10²
x² + 64 = 100
x² = 36
√x² = √36
x = 6

Line x bisects the chord with length into equal halves.
⇒ Half the cord = 16 ÷ 2 = 8 units

Radius = Diameter ÷ 2 = 20 ÷ 2 = 10 units

With the 2 lengths, we can use Pythagorean Theorem to find x:

a² + b² = c²

x² + 8² = 10²

x² = 10² - 8²

x² = 36

x = √36

x = 6 unit

x = 6