Just right click and delete

I suggest the following:

1) Right-Click on the task bar, select Properties
2) On the Taskbar tab, you will see "Show Quick Launch" (5th item) box;
3) Remove the tick from here
4) Click OK

HTH

Please clarify exactly what you mean by "the left hand side of the
task bar."

If you mean the "Quick Launch Bar," just right-click on the icon on
choose "delete."

Note however that the Quick Launch Bar is not necessarily "the left
hand side of the task bar." In fact the Quick Launch Bar doesn't have
to be on the Task Bar at all, and can be dragged off it and docked on
another side of the screen entirely.