How do I know if my service panel will accommodate a 240v circuit breaker
The panel can indeed support a 240V breaker. The question you should ask is, is there space in the panel to physically accommodate additional breakers?
Based on the model number, your panel should look something like this.

Notice how this example image has lots of blank spaces. In a panel like this, there's no problem at all installing a new breaker (or double pole breaker in your case). However, it's not likely your panel looks like this. More probable, is your panel has all or nearly all the slots full.
If there are not two free spaces in the panel, you'll not be able to install a new breaker in this panel. You have a few options in this case.

Install tandem breakers where possible to free up slots.
Install a subpanel.

The other problem you could have, is that your current service will not handle the additional load.  This panel can handle 100 amperes, but that does not mean you have 100 amp service. You'll have to check with the local utility to determine the size of the current service. If
Lastly, the panel might already be close to being overloaded. If you have all electric appliances (Range, Dryer, heat, water heater, etc.), adding a hot tub could cause the main breaker to trip from time to time. This will completely depend on your current consumption of power, which is not possible to know based on the information you've provided.
tl;dr
Contact a local licensed Electrician to determine what's required with installing a hot tub.