"Cast", as in "throw", as if you were fishing. "Back" refers to the past, specifically an experience in your past. "Cast your mind back to (time in the past)", which means to recall a past event. Moreso, the phrase suggests that you imagine yourself back in time, at that moment.

Something had that happened in the past. Which don’t have might remember very well. But it’s try to remember as much as possible.

it's American Idiom If somebody tells you to cast your mind back on something, they want you to think about something that happened in the past, but which you might not remember very well, and to try to remember as much as possible.