The short answer is probably or at least maybe, but I do not have that device so I can't say for sure.
According to sony's specs (https://store.sony.com/p/Sony-Cyber-shot-Touch-Screen-Camera/en/p/DSCTX66#specifications), that camera will accept a micro SDHC card (This is an SDXC). I just don't know enough details about the camera to know if it will accept the SDXC without issues. According to other shopping sites (yahoo - http://shopping.yahoo.com/961262380-cyber-shot-dsc-tx66-silver-digital-camera-182-mp-5x-opt-ms-duo-ms-pro-duoms-pro-hg-duosdsdhcsdxc-card-slot/), the camera will accept it.
You can reformat the card if you know what you are doing and then it would definitely work (assuming the camera can read cards this large). More information about SDHC vs SDXC and compatability can be found here: https://en.wikipedia.org/wiki/Secure_Digital
Yes, the memory card should work just fine. SDXC is an extension of SDHC, and all devices that are SDHC compatible should read the newer format just fine, some just won't be able to access the entire capacity. I looked at the Sony website for that product, and saw that it is SDHC compatible. I say, "Go for it!"
As far as I concern, this product can be used in cells , pad (tablet), if you use it in camera, you'd better ask the service of sandisk . The goods was optimise for Android system, if you use it for samsung camera (newest type ,used Android system) maybe it's ok.
I honestly don't know. If the Cybershot does "take" micro sdcards. I would check to see if it has a memory limit. If not, I'd buy it/use it in my Canon sd970. This card came with a "sdcard shell" which means it doesn't matter if the camera takes a standard size SD card, or micro as discussed above. Good luck.