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A Durham Mug template size is 22cm x 9cm (approx).  Manufacturers of mugs vary the sizes slighly, but if you create a template at this size and the printing requires that the size is adjusted, it will only be slightly and un-noticeable.

22cm at the standard screen resolution of 72dpi is 625 pixels
9cm at the standard screen resolution of 72dpi is 255 pixels

 

So your image will need to be: 625 x 255 pixels

If you would like to make your template a much higher resolution use multiples of the ratio to make the image larger.  This way the image stays in propotion when the printer makes it fit the Mug.
ie,
1250 x 510 pixels
2500 x 1020 pixels

Open Microsoft Paint and click file>new or press (Ctrl+N)

Now select  Resize from the toolbar and a popup window will appear called "Resize and Skew".

Select the radio button for pixels.

De-select Maintain Aspect Ratio.

In the Horizontal box type:  625
In the vertical box type:  255

Click OK