Reading the entirety of the exercise, you are asked to find the amount of oil that he'd started with. So perhaps do your definition as:

[imath]\qquad \textrm{the amount of oil in the begining: } x[/imath]

Then work day-by-day. For instance, at the end of Monday:

[imath]\qquad \textrm{two-thirds sold, so one-third left: } \frac{x}{3}[/imath]

Then look at end-of-business on Tuesday:

[imath]\qquad \frac{4}{9}(\frac{x}{3}) - 340[/imath]

[imath]\qquad \frac{4x}{27} - 340[/imath]

Continue, simplifying as you go. Set your final expression equal to the amount that he kept for himself. Solve that equation.

Monday: Eddie sold 2/3 of his oil, so he had $x - 2/3x = x/3$ left.

Tuesday: 4/9 of the remainder, which is 4/9 * x/3 = 4x/27. He also sold an extra 340 liters, so he had $x/3 - 4x/27 - 340 = 7x/81 - 340$ left.

Wednesday: 1/2 of the remainder, which is 1/2 * (7x/81 - 340) = 7x/162 - 170. He also sold an extra 200 liters, so he had $7x/162 - 170 - 200 = 7x/162 - 370$ left.

Thursday: kept the remaining 1260 liters of oil, so we have the equation:

7x/162 - 370 = 1260

are you sure that is how you solve it? The answer I’m getting is 3503.33

I wasn't paying attention, and switched my meaning on Tuesday. Sorry!

Yes, at the end of Monday, there remains [imath]\frac{x}{3}[/imath] of the original amount of oil.

On Tuesday, he sells [imath]\frac{4}{9}[/imath] of what was left at the end of Monday, so he still has [imath]\frac{5}{9}[/imath] of what he had at the end of Monday, or [imath]\frac{5x}{27}[/imath]. Then he sells an additional [imath]340[/imath] units so, at the end of Tuesday, he has [imath]\frac{5x}{27} - 340[/imath] units available.

On Wednesday, he sells half of what was left, so he still has half:

[imath]\qquad \frac{1}{2}\left(\frac{5x}{27} - 340\right) = \frac{5x}{54} - 170[/imath]

Then he sells another [imath]200[/imath] units so, at the end of the day, he has the following amount left:

[imath]\qquad \frac{5x}{54} - 170 - 200 = \frac{5x}{54} - 370[/imath]

At this point, he has [imath]1260[/imath] units left, so:

[imath]\qquad \frac{5x}{54} - 370 = 1260[/imath]

[imath]\qquad \frac{5x}{54} = 1630[/imath]

[imath]\qquad 5x = 88020[/imath]

[imath]\qquad x = 17604[/imath]

Checking:

On Monday, he sold [imath]\frac{2}{3}[/imath] of what he had, so he kept [imath]\frac{1}{3}[/imath]:

[imath]\qquad \frac{1}{3}(17604) = 5868[/imath]

On Tuesday, he sold [imath]\frac{4}{9}[/imath] of the [imath]5868[/imath] units, so he had [imath]\frac{5}{9}[/imath] left:

[imath]\qquad \frac{5}{9}(5868) = 3260[/imath]

Then he sold another [imath]340[/imath] units:

[imath]\qquad 3260 - 340 = 2920[/imath]

On Wednesday, he sold [imath]\frac{1}{2}[/imath] of what was left, which means that he still had half of what was left:

[imath]\frac{1}{2}(2920) = 1460[/imath]

Then he sold another [imath]200[/imath] units, so he was left with [imath]1260[/imath] units, as required.

(P.S. Normally, a solution would not / should not be posted so soon, but I steered you wrong, so I felt obligated. Again, apologies for the confusion.)