What is meant by number of ways in Panelboard?
How does it impact if the panel board has
a) Single pole circuit breakers and a common neutral bus (230V Line to Neutral)?
b) Double pole breakers (230V Line to Line)
c) Double Pole breakes (230V Line to Neutral)
Is the quantity of breakers has to be multiples of 3 in any panel board?
I'm not familiar with the term "number of ways" in a panelboard, but two possible meanings are the number of spaces in the panelboard, or the number of phases in a panelboard.
The QTY of spaces comes in multiples of 3 in a 3-phase panelboard.
The QTY of spaces comes in multiples of 2 in a split-phase (also called single phase) panelboard. It could be both a multiple of 2 and a multiple of 3.
QTY of spaces means the number of possible single pole (non-tandem) breakers that can fit in the panel. You do not necessarily use all possible spaces, as there are filler plates or break-away tabs that can fill unused breaker positions.
The line-to-line voltage will not be the same as the line-to-neutral voltage.
In a 3-phase WYE system, the most common type of 3-phase system at the end-user's level, the line-to-line voltage will equal sqrt(3) * the line-to-neutral voltage. Examples are 120/208V three-phase, 277/480V three-phase that are common in the US, and 230/400V that is the most common in the rest of the world. The smaller voltage is line-to-neutral, and the larger voltage is line-to-line. A single pole breaker plus a neutral connection will establish a branch circuit that is of the line-to-neutral voltage. A 2-pole breaker connected to two separate phases, will establish a single phase circuit of the larger voltage. Some 2-pole loads also use the neutral, like electric dryers that use 208V to power the heating and 120V to power the motor. You can also power 3-phase branch circuits, with 3-pole breakers that connect to all three lines and the neutral.
In a split-phase system, the line-to-line voltage will equal twice the line-to-neutral voltage. In the US, this as a 120/240V split-phase system is typical of most single family and duplex residences, where each property gets a single phase delivered to them, and the secondary of the transformer is center-tapped. You get a black wire that powers the Line 1 circuits, and a red wire that powers the Line 2 circuits, and a white wire for the neutral from the center-tap that is grounded at the service disconnect. Line 1 and Line 2 are equal and opposite in voltage (which is mathematically equivalent to 180 degrees out of phase), hence the difference between them is twice the line-to-neutral voltage.
