You can't count event triggers directly, but you can count them indirectly by counting the captures resulting from the triggers (which, if you have set up the trigger correctly, and the events are not too close to each other, should amount to the same thing) and there are a number of methods that you can use to do that in PicoScope 6.
First, you need to be aware that PicoScope 6 uses 2 different Modes of capturing samples - Fast Sampling Mode and Slow Sampling Mode. In Slow Sampling Mode the samples are effectively streamed to the Computer from the Hardware PicoScope in real time, because the sample rate is slow enough to do that without missing data. In Fast Sampling Mode the samples have to be buffered in the hardware first and then sent to the computer, when the capture is complete, to avoid missing data. So, in general, the Faster Timebases are set to use Fast Sample Mode, and the Slow ones use Slow Sample Mode (but can be changed).
In 'Fast Sampling Mode', the main method for counting captures would be to set the 'Trigger Mode' to 'Repeat Trigger', set the 'Maximum Waveforms' for the 'Waveform Buffer' in the 'Tools->Preferences' Menu option to 10,000, and then just observe the number of waveforms that have been captured in the display for the 'Waveform Buffer Index' (next to the Compass icon). However the total number of waveforms you will be able to capture will depend upon the model of PicoScope that you have (i.e. limited by the size of the buffer in your hardware PicoScope), the number of waveforms you are capturing (the absolute maximum being 10,000), and the number of samples that you are storing per capture. You can see the number of samples that you will be capturing by turning on the properties 'View pane' (go to the 'Views' menu and select 'View Properties'). Also, when using this method, the minimum time between triggers for reliable triggering will be between 5ms to 10's of milliseconds (depending upon PicoScope model, data size, USB availability, and transfer rate).
For a smaller minimum time between triggers, i.e. <1us to a few microseconds you can set the 'Trigger Mode' to 'Rapid Trigger' instead, and increase the number of captures that you will get to the maximum in the 'Rapid Captures' Text box (next to the black Rabbit icon, at the bottom of the display). However, this would only be applicable to your measurement goals if you need to capture very closely spaced events that also occur extremely infrequently (this method would also have the buffer limits mentioned for the method using 'Repeat Trigger Mode'). Also, not all of our PicoScope models have Rapid Trigger Mode.
In 'Slow Sampling Mode', you can also use 'Repeat Trigger', to see the number waveforms captured for your trigger conditions (as mentioned for Fast Sampling Mode) but the difference will be that the maximum number of samples you can capture in total will be 10M samples. However, you can reduce the number of Timebases that use Slow Sampling Mode by going to the 'Sampling' tab in Preferences and increasing the 'Collection Time' under 'Slow Sampling Transition'. This will allow you to use the full size of your hardware buffer, instead of the 10M limit, for the extra Timebases that are faster than the altered 'Slow Sampling Transition' value.