Does Anyone Know The Approximate Value Of This Coin?

No, discussion of and questions about "what's the value" are best kept in the regular discussion areas of the forum, for that country, since those parts of the forum are likeliest to attract the attention of people who actually know the answer to your question.

As for the specific question on your coin, the table of catalogue values (in the Krause catalogue) for this coin can be seen here. It's hard to judge the condition of your coin from those pics, but I'd guess somewhere around VF-EF; that would give it a book value somewhere around $10. Also note the coin is made of 50% silver, so the minimum price is bullion value, 60 US cents.

Just to note: from 1937 to 1944, Britain issued two different kinds of threepences, which circulated side-by-side: the small silver one and the large 12-sided brass one. By 1942, the silver ones were being phased out due to wartime hoarding and the mintages were dropping. It's not "scarce", but it's by no means "common", either.

No disrespect but that is marginal F (UK).The reverse always look less worn on this series.The obverse has lost most detail.
I wouldn't put it on ebay by itself at a 99p start because it probably wouldn't sell.
Another snippet is that 1942,43 & 44 were only issued for Colonial use.The 1944 IMO is the most overvalued 20C UK coin.

from Collectors coins GB
F £1, VF £6, EF £14, UNC £30

Another catalogue I have has similar prices.