I think you'll find it's actually
> Trespass Damaging underwood fine / 2
(I'm assuming it is the second of the two similar offences shown)
" _Underwood_ " in this contest was the small trees & shrubs that grew beneath the taller _timber_ trees.
If the fine wasn't paid, then a prison sentence would follow. This is what I suspect has happened to your ancestor.
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If you look in this volume of Accounts and Papers of the House of Commons, there is an example on page 617 from the returns of Berkeley in Gloucestershire where the listed offences included " _damaging underwood_ ". The entry also has a column showing the " _Maximum and Minimum Term of Imprisonment if Fine not paid_ ".
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It is also worth checking the British Newspaper Archive for 1844 to see whether the conviction made the local papers. If so, it is possible that will give you further detail or context.