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I open 1C -- Partner 1D -- I respond 1S -- Partner bids 2NT - What 2NT means, and how do I respond to it with this hand: Kxxx-Kx-xx-AQxxx?
Note: since I'm studying simple sayc what concerns me is whether I can bid "pass" here (my considerations were: I don't have 5 spades so we don't have fit, and also since the partner didn't bid 3NT - he doesn't have enough points for game together with my 12 so, nothing left for me to show else here).
In this context 2NT is an invitation to game. Your partner probably has around 11-12 points, so he doesn't know if you have enough points between you to make 3NT (you haven't bid anything that shows more points than the bare minimum needed to open).
As your hand is pretty weak you should pass. If you had 14 or more points then you would bid 3NT.
Assuming that you play 4th Suit Forcing (and possibly artificial), then partner has denied game-forcing values by choosing not to bid 2H. This means that the 2NT bid is invitational, and you should pass to show your minimum.
A hand only a bit better that could consider continuing to 3NT is KT9x-Kx-Tx-AQT9x. Now the extra T's and 9's significantly raises the chance of one black suit running quickly, and vulnerable at IMPs I think a shot at 3NT is justified. You are probably still short of the 50% likelihood needed to consider continuing to 3T in MatchPoints or white at IMPs.
In an auction that starts 1C-1D; 1S, responder might have any of the following types of hands:
4D and 3H on this sequence are not mentioned in the SAYC, but it seems right to treat them as I have mentioned. 5NT grand slam force is old-fashioned but is required by the SAYC booklet.
You'll notice that 2H shows a lot of different hands; the rest of the auction should clarify your hand to your partner; it's important that they make negative inferences based on the fact that you didn't take a different bid on your second turn. In SAYC 2H is forcing for one round; many/most partnerships form an understanding that when responder bids the fourth suit, it is game forcing (except 1C-1D-1H-1S).
The bids listed in the minimum section are signoffs, though partner may correct to a different signoff based on their shape (e.g. they may pull 1NT to 2C or 2D).
With a response of 1d, partner may have as little as 6-9 points (minimum responding values).
When you rebid 1s, and partner said 2NT, he showed a two response hand of 10-12 points, just below values for an opening hand, but without four spades, since he didn't raise them. Probably a true balanced NT type hand with 2-3 spades opposite your four, 4-5 diamonds, 2-3 clubs, and the rest hearts.
There is a saying that an opening hand opposite an opening hand can make game. That is true if there is a "fit," and you both have something to spare.
In your case, you have a BARE minimum opening hand with 12 HCP points, and partner is showing a SUB-minimum opening hand of 10-12. You probably have 22-24 between you, and no major suit fit, with NT probably being your best spot. You should stop at 2NT, and hope to make eight tricks. Nine is possible, but a stretch.
With a bit more, say the Q of diamonds opposite his, or AQJTx of clubs instead of what you have, I'd raise to 3NT.
