What will happen in ice-hockey if both teams get a penalty and the play is 4v4 and then a little fight occurs resulting in 2-minute penalties for one player from team A and one player from team B at the same time. Will the 4v4 play continue or will it be 3v3?
The 4v4 play continues. NHL Rules (PDF):
19.1 Coincidental Minor Penalties - When coincidental minor penalties or coincidental minor penalties of equal duration are imposed against players of both teams, the penalized players shall all take their places on the penalty benches and such penalized players shall not leave the penalty bench until the first stoppage of play following the expiry of their respective penalties. Where goalkeepers are involved, refer to 27.1. Immediate substitution shall be made for an equal number of minor penalties or coincidental minor penalties of equal duration to each team so penalized and the penalties of the players for which substitutions have been made shall not be taken into account for the purpose of the delayed penalty rule (Rule 26 – Delayed Penalties). This rule only applies when at least one team is already serving a time penalty in the penalty box that causes them to be short-handed..
When one minor penalty is assessed to one player of each team at the same stoppage in play, these penalties will be served without substitution provided there are no other penalties in effect and visible on the penalty clocks. Both teams will therefore play four skaters against four skaters for the duration of the minor penalties.
Should one or both of these players (or any other players) also incur a misconduct penalty in addition to their one minor penalty, this rule shall apply and the teams would still play four skaters against four skaters (the player incurring the misconduct penalty would have to serve the entire 12 minutes – minor plus misconduct – and his team would have to place an additional player on the penalty bench to serve the minor penalty and be able to return to the ice when the minor penalty expires).
When multiple penalties are assessed to both teams, equal numbers of minor and major penalties shall be eliminated using the coincidental penalty rule and any differential in time penalties shall be served in the normal manner and displayed on the penalty time clock accordingly (see 19.5). If there is no differential in time penalties, all players will serve their allotted penalty time, but will not be released until the first stoppage of play following the expiration of their respective penalties.
For coincidental penalties that carry over into, or are assessed during regular-season overtime, refer to 84.3, to Reference Tables – Table 17 – Penalties In Effect Prior to the Start of Overtime – Regular Season on page 160, and to Reference Tables – Table 18 – Penalties Assessed in Overtime – Regular Season on page 161
So if one team is already serving a penalty, they offset or delay additional penalties such that it is always either 4v4 or 4v3 at worst. They will first try to offset. In an offset, the player goes to the penalty box but the team may substitute another player. Players serving penalties but having substitutes cannot enter the ice until play stops. Players may only enter the ice if their penalties leave the team short-handed.
If they can't be offset because one team has more than two penalties more than the other team, then they will delay the penalty (see Rule 26). A delayed penalty means that the penalized player is off the ice for the length of not only that player's penalty but the delay period. But the team will still be able to play a substitute for the delayed player until that player's penalty starts.
A team will never have fewer than three players (four including the goalie) on the ice at once. And the only time it will be 3v3 is in overtime. Offsetting penalties never take it below 4v4.
The confusing part here is that the first penalties don't offset. That's what takes from 5v5 to 4v4. But additional penalties do. So in regular play, the game will be 5v5 (no penalties), 5v4 (one penalty), 4v4 (any number of penalties such that both teams have the same number), 5v3 (one team has two or more penalties while the other has none or where one team has at least two more penalties than the other), 4v3 (one team has one more penalty than the other).
In regular-season overtime, the base is 3v3 and they add players to the ice when there are penalties that are not offset. If the teams have offsetting penalties they will play 3v3. In the playoffs, overtime is played the same as regulation play.