When I touch two pieces simultaneously, how will the touch move rule apply? How is this rule used for this situation? I could not find any resources to do with this situation.
When I touch two pieces simultaneously, how will the touch move rule apply?
It will primarily depend on your intention, or rather what onlookers clearly perceive as being your intention.
Here's what the latest FIDE Laws of Chess have to say:
4.1 Each move must be played with one hand only.
4.2.1 Only the player having the move may adjust one or more pieces on their squares, provided that he first expresses his intention (for example by saying “j’adoube” or “I adjust”).
4.2.2 Any other physical contact with a piece, except for clearly accidental contact, shall be considered to be intent.
4.3 Except as provided in Article 4.2, if the player having the move touches on the chessboard,with the intention of moving or capturing:
4.3.1 one or more of his own pieces, he must move the first piece touched that can be moved
4.3.2 one or more of his opponent’s pieces, he must capture the first piece touched that can be captured
The firs thing to note is that of you used two hands then that will be punished as an illegal move (article 7.5.4).
If it is clearly accidental then you will be permitted (required) to move the piece that it was clearly your intention to move. An example of this is something which sometimes happens to me when I reach across the board to move a piece on the far side and my forearm brushes and sometimes knocks over the tallest piece on my side of the board, my king.
So, that leaves cases where you deliberately touched two pieces simultaneously with one hand. There are two articles which deal with that in the laws, one more draconian than the other and so far less likely to be invoked.
11.5 It is forbidden to distract or annoy the opponent in any manner whatsoever.
If an arbiter saw you do this (deliberately touch two pieces simultaneously with one hand) then they would likely immediately warn you. If the opponent claimed that it was an annoyance you might receive more than a warning.
Repeat infringements would put you at risk of:
11.7 Persistent refusal by a player to comply with the Laws of Chess shall be penalised by loss of the game. The arbiter shall decide the score of the opponent.
In extreme circumstances (I cannot think of any time this has been invoked) the arbiter could punish you under:
11.1 The players shall take no action that will bring the game of chess into disrepute.