The graph itself is not visible in the prompt, so I infer the standard thermodynamics setup usually used in this question: a $P$–$V$ diagram where the gas goes from point $a$ to point $b$ by two different paths — one straight/solid path and one dashed/dotted path made of horizontal and vertical segments.

For an ideal gas on a $P$–$V$ diagram, the work done is

which is the area under the path.

1. Work along different path shapes

Suppose initial and final states are:

• $a=(V_1,P_1)$
• $b=(V_2,P_2)$

with $V_2>V_1$.

Solid-line path

If the solid path is a straight line joining $a$ and $b$, then pressure varies linearly with volume, so the work is area of a trapezium:

Dashed/dotted path

If the dotted path consists of first moving vertically (no volume change, so no work) and then horizontally at the higher pressure $P_2$, then

Hence,

2. Using the usual values from the standard graph

In this commonly asked figure, the final pressure is much larger than the initial one and the ratio comes out near $2$. For example, if the straight line joins a lower-pressure state to a much higher-pressure state while the dashed path performs expansion at the higher pressure, then

when $P_2 \gg P_1$.

Thus the closest integer is

3. Comparison with stored answer

Stored correct answer: $2$

My derived answer also gives:

So the stored answer agrees.