Start by examining the consequences of any checks you can give: our modus operandi. There are four: Ne6 (does nothing), and Qf8, Qg8, and Qh8. Qf8 can be dismissed immediately as it results in RxQ with no gain. Qg8 is unhelpful because it is met with KxQ, drawing the king to a light square; since all White has is his knight, and since the knight and Black’s queen already are on dark squares, it should be obvious that you would like to draw Black’s king onto another dark square as well. Qh8 accomplishes the mission, forcing KxQ (if the king instead moves to g6 or h6, White plays QxQ, as should be obvious if you are visualizing the White queen on h8; it’s yet another skewer). Now the White knight and the Black royals are arranged for a fork via NxR+.

Another way to see this would be to start with the knight and notice from the pattern of its relationship to the Black king and queen that it is just one move from attacking either of them, but that they cannot be attacked at the same time. To achieve a simultaneous attack, one of them would need to be drawn onto a different dark square. This can be done by moving your queen to a square where you want the king to move, and from which your queen gives check (and skewers the Black queen to boot, thus requiring Black to play KxQ and walk into the fork).