I am trying to get some extra space in my panel and am having a hard time finding a tandem breaker that will fit in this box (see photo), can anyone help?
That looks to be a Siemens load center into which someone has plugged in a single Square D Homeline breaker. Physically they fit, but it is unlikely that the Sq. D breaker is listed to be used in a Siemens panel and I guarantee the Siemens panel is not listed for using Square D breakers. But that's not what you asked...
As to the tandems issue, Siemens panels must be specifically designed to accept tandems because the bus connections are different. As others have said, the label on the inside of the door of the panel will list the options you have available to breakers.
But the quick way to tell is to look at the part number for the panel. There will be a letter (or 2) followed by 4 digits, then some other stuff. The 4 digits immediately after the letters tells you what you can do in this regard. The first pair of digits tell you the number of "spaces" in the panel, the next pair of digits tell you the number of "circuits" it can handle. If the two sets of numbers are the same, the panel CANNOT accept any tandem breakers, i.e. "ES1212..." means it is 12 spaces, 12 circuits, meaning NONE of the spaces will allow a tandem breaker. If the part number is "ES1624..." it means it has 16 spaces, but will allow up to 24 circuits, so that means that 8 of the available spaces (usually at the top only) can accept tandems, meaning you end up with 16 circuits in those top 8 spaces using tandems, then 8 more single breakers in the bottom 8 spaces.
All we can see is QP and hom breakers we need to see the texts printed on the panel to provide help. The breakers need to be listed for the panel. , since this information is lacking a code compliant recommendation is impossible. Square D panel has Non CTL breakers and double stuff breakers but we need to know the type of panel to suggest a code compliant breaker.
Added with the panel photo; that is a 40-40 panel so you can not use double stuff or cheaters. The proper path forward would to be to add a sub panel to the side. Remove 2 breakers from that panel and use those slots to install a feeder breaker to your sub. The wires for those 2 breakers including the neutrals and ground can be pigtailed or spliced and pulled into the sub then hooked back up. You will need a 4 wire feeder 2 hot 1 neutral and 1 ground to the new sub panel. The ground and neutral need to be isolated so if your new panel has a bonding screw or copper jumper that would need to be removed. This is the only code compliant way to proceed with that panel.