2♣ Stayman

The 2♣ Stayman is a conventionnal bid.
In response to a 1NT opening, a 2♣ bid is a Stayman, looking for an eight-card fit in a major suit. It promises:

at least 8 HCP
and at least 4 cards in one of the majors. It is also used with both majors, 4-4 or 5-4.

Avoid using this convention when you hold a 4333 hand with scattered honors. These hands are too balanced to work well in a trump game. You'd rather play a NT game (9 tricks instead of 10)
2♣ Stayman is forcing for one round, indeed !

S	W	N	E

Problem E2068 2♣ First, try to find a ♥ fit. With at least 8 HCP, start bidding 2♣ (Stayman) to look for a fit in one of the majors. That's a priority !

S	W	N	E

Problem E2062 3NT Even though you've got 4 ♠ cards, don't use the Stayman 2♣ conventional bid. You have a balanced hand, no ruffing added value. Your pair's points are 25-27 HCP. Try a NT game.

Bidding development : the opener's rebid after his partner's 2♣.

2♦ when he has no 4 card major
2♥ with 4 ♥ cards (or 2♠ with 4 ♠ cards)
2♥ with both 4 ♠ and 4 ♥ cards. The opener has the option to bid ♠ later if his partner's 4 carder happens to be ♠. Many players bid 2NT to indicate both majors, but this is giving useful (but unnecessary) information to the opponents.

The responder's 2nd bid after the opener has named a major suit.

With 8 HCP the responder proposes game in NT or in the major suit (when there is a fit, of course). The opener will pass with a minimum hand (15 HCP) or go to game if maximum.
With 10 HCP or more the responder goes directly to game either in NT or in the fitted major. The pair's combined points are enough for game (minimum 15 + 10 = 25)