Well, after a deep dive into the provided YouTube link, which appears to be YouTube's corporate page in Japanese, I can confidently report that your coin's value remains a complete mystery according to that source. Let's set that aside and get to the real silver lining.
Your 1968 half dollar is an interesting piece from a transitional era in U.S. coinage. Think of it as the awkward teenager of Kennedy halves. It's not the 90% silver powerhouse from 1964, but it hadn't yet given up on precious metals entirely like the coins after 1970. This means your 1968 half dollar is composed of 40% silver.
Because of this silver content, your coin is always worth more than its 50-cent face value. Its base value is tied directly to the fluctuating price of silver. This "melt value" is its absolute floor, typically hovering somewhere in the $3 to $5 range, depending on what the market is doing that day. It's the coin's built-in "I'm better than a modern quarter" price tag.
Now, could it be a hidden treasure? It's unlikely. The Denver mint pumped out over 246 million of these in 1968, so they aren't exactly rare. A common, circulated coin that has seen its share of pockets and cash drawers is worth its silver melt value and not much more. However, if you have a brilliant, uncirculated specimen that looks like it just rolled off the press yesterday, a collector might pay a premium, perhaps pushing its value toward the $10 mark or slightly more for a truly exceptional, graded example.
