"Did you really think you could do something that will checkmate the king?"
And is it correct to use (can) instead of (could) in the sentence above? if so, would they mean the same?
" This is talking about the past. " This is talking about now and the future. We usually tak about checkmating our opponent, not his king.
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"Did you really think you could do something that will checkmate the king?"
OK, but more standard is
"Did you really think you could do something that would checkmate the king?" This is talking about the past.
"Do you really think you can do something that will checkmate the king?" This is talking about now and the future.