The numbers refer to rules in the FIDE laws of chess.
6.2. A player must press his clock with the same hand with which he made his move. It is forbidden for a player to keep his finger on the clock or to ‘hover’ over it.
The rule that you have to press the clock with the same hand that you use to move the pieces is there to prevent players from pressing the clock before they have completed the move: if one is in such a time trouble that this rule matters, he/she would very probably, perhaps unconsciously, press the clock before he has clearly released his hand from the piece if this rule was not enforced. Nobody wants to see their opponent's hand over the board when their clock is running and they need to make a move quickly.
Often, the player with the black pieces is allowed to decide which side of the board the clock is on. Technically, the arbiter may place the clock on the side of the board where he sees it better [rule 6.5]. Often the player with the black pieces may choose on which side of the board he sits on, amounting to the same. (But this is no longer a rule in the Fide laws; some tournaments may not allow even doing that, for example because of carefully adjusted digital boards; in these cases the clock is almost always on the queenside (black's right hand side and white's left hand side).