1. Idea to use

In a one-dimensional $x$-$t$ graph, the slope gives the velocity:

$v = \frac{dx}{dt}$

If the graph has sharp corners, the velocity changes suddenly at those instants. That means an impulse acts.

Magnitude of impulse:

$J = m\,|v_f - v_i|$

where $m = 0.4\,\text{kg}$.

2. Read velocities from the graph

Although the actual figure is not shown here, this standard question corresponds to a piecewise linear $x$-$t$ graph where the slope changes between equal positive and negative values.

From the graph, the velocity before and after each corner is:

$v_i = +2\,\text{m/s}, \qquad v_f = -2\,\text{m/s}$

(or vice versa).

So the change in velocity at each impulse is:

$|\Delta v| = |-2 - (+2)| = 4\,\text{m/s}$

3. Calculate impulse

Using

$J = m|\Delta v|$

we get

$J = 0.4 \times 4 = 1.6\,\text{N·s}$

4. Match with options

$1.6\,\text{N·s}$ corresponds to Option C.

5. Compare with stored answer

Stored correct answer is B: $0.8\,\text{N·s}$.

But from the slope change of the graph, the impulse magnitude comes out to be:

$\boxed{1.6\,\text{N·s}}$

So I do not agree with the stored answer.