The position of a particle moving on the X-axis is shown as a...

The velocity of the particle is given by the slope of the position-time ($x-t$) graph, $v = \dfrac{dx}{dt}$.

Analyzing Option (1): The slope of the graph alternates between positive and negative values between $t = 0$ and $t = 6 \text{ s}$. It is not continuously positive. Hence, option (1) is incorrect.

Analyzing Option (2): The average velocity is defined as the total displacement divided by the total time, $v_{\text{avg}} = \dfrac{x_f - x_i}{\Delta t}$. From the graph, the initial position at $t = 0$ is $x_i \approx 15 \text{ m}$, and the final position at the end of the shown period is $x_f \approx 12 \text{ m}$. Since $x_f < x_i$, the total displacement is negative, which means the average velocity is negative. Hence, option (2) is correct.

Analyzing Option (3): The speed is the magnitude of the velocity, which corresponds to the steepness (absolute value of the slope) of the $x-t$ graph. The steepest slope occurs around $t = 2.2 \text{ s}$ or $t = 3.8 \text{ s}$, not at $t = 6 \text{ s}$. Hence, option (3) is incorrect.

Analyzing Option (4): The particle comes to rest when its velocity is zero, which corresponds to the points where the tangent to the $x-t$ curve is horizontal (local maxima and minima). Counting these turning points on the graph, there are exactly $6$ such points (three minima and three maxima). Hence, option (4) is correct.