target display not working

But which year Macs & OSes on both ends?

iMac models introduced in 2011, 2012, 2013, and mid 2014

To use any of these iMac models as an external display:

• The iMac used as a display must have macOS High Sierra or earlier installed.
• The other Mac that you're connecting it to must have been introduced in 2019 or earlier and have macOS Catalina or earlier installed.
• The cable connecting the two Mac computers must be a Thunderbolt  or Thunderbolt 2  cable.

24-inch and 27-inch iMac models introduced in 2009 and 2010

To use any of these iMac models as an external display:

• The iMac used as a display must have macOS High Sierra or earlier installed.
• The other Mac that you're connecting it to must have been introduced in 2019 or earlier and have macOS Catalina or earlier installed.
• The cable connecting the two Mac computers must be a Mini DisplayPort  cable.

• Make sure that your iMac is using macOS High Sierra 10.13.6 or earlier. You can't use target display mode with later versions of macOS, or with Boot Camp and Windows.

According to your signature you are running Monterey 12.0 which does not meet the criteria.

What if the case my iMac (External monitor purpose) and Mac (work PC) both were running in Monterey 12.0 ? Please help !

Nope, Monterey on just 1 puts it out of reach.