You know that your object starts from rest, which means that tis initial velocity will be equal to zero.
Moreover, it has an uniform acceleration of 4 "m/s"^2. To determine its displacement, you can use this equation
d = v_0 * t + 1/2 * a * t^2, where
t - the object's time of travel;
a - its acceleration.
In your case, you have
d = underbrace(v_0)_(color(blue)("=0")) * t + 1/2 * a * t^2 = 1/2 * a * t^2
Point (1)
After 5 seconds, the object's displacement will be
d = 1/2 * 4"m"/cancel("s"^2) * 5^2cancel("s"^2) = color(green)("50 m")
Point (2)
To determine how much the object travelled in the 5^("th") second of movement, you need to subtract the distance it travelled after 5 seconds from the distance it travelled after 6 seconds.
Deltad_(5,6) = d_6 - d_5
d_6 = 1/2 * 4"m"/cancel("s"^2) * 6^2cancel("s"^2) = "72 m"
d_5 = "50 m"
Deltad_(5,6) = 72 - 50 = color(green)("22 m")
Point (3)
The same method can be used to determine the distance the object travelled in its 8^("th") second of movement.
Deltad_(8,9) = d_9 - d_8
d_9 = 1/2 * 4"m"/cancel("s"^2) * 9^2cancel("s"^2) = "162 m"
d_8 = 1/2 * 4"m"/cancel("s"^2) * 8^2cancel("s"^2) = "128 m"
Therefore,
Deltad_(8,9) = 162 - 128 = color(green)("34 m")
