The sponsor card "Foreign Institute" needs strength 6, so you can play it when your action-card "sponsor" is on 5 (if it is already turned to the red side which adds 1 strength).
If it is on position (=strength) 3, you need 2 X-tokens to play it - or you discard 1 card from your hand.
In one of my running games the sponsor was on position 5 (and turned to the red side). I had two sponsor cards (for strength 5 and 6) and I could play both of them with 3 X-tokens and 1 discarded card: 5 (position) + 1 (red side) + 3 (X-tokens) + 2 (discarded card) = strength 11. Quite a powerful ability.