The table isn't right. There are TD and TR tags sprinkled a little at random.
CODE
<table>
<tr>
<td>
<tr>
The last TR above has nothing there to do. Remove it. The TD is superfluous too since you have a TD below.
CODE
<td>One</td>
<td>Two</td>
<td>Three</td>
</tr>
<tr>
<td>Four</td>
<td>Five</td>
<td>Six</td>
</tr>
<tr>
<td>Seven</td>
<td>Eight</td>
<td>Nine</td>
</tr>
</td>
The above is fine upto the last </td>. Remove it.
CODE
<td>
<img src="test.png" />
</td>
This is all wrong because it isn't in a table row.
CODE
</tr>
</table>
That's the correct way to finish a table.
If you want the image to the right of the text cells you need to add one more column. That means one more cell in one of the rows. The first seems suitable.
CODE
<table>
<tr>
<td>One</td>
<td>Two</td>
<td>Three</td>
<td rowspan="3"><img src="test.png" /></td>
</tr>
Since you have three rows in the table but want to melt the rightmost cells together for the image you use rowspan="3".
The principle is this. TABLE contains a number of TR. Each TR can contain a number of TD. The elments must come in that order. The TDs must add up for each row and each column (it's a grid). You use colspan or rowspan to melt cells together to a larger cell.