I’ll try my best:
First, start a metronome on 120 bpm.
To explain the multiplier you have to keep in mind what a time signature means. What is 4/4?
The lower number represents the figure of your pulse. That means you should hear the constant sound of a metronome as a quarter note. The upper number represents the amount of quarter notes you can fit in a measure (in this case, 1, 2, 3, 4).
When you multiply the lower number by 2, the constant pulse of a metronome should now be heard as eighth notes (1 and 2 and). The reason why the counting stopped at the fourth pulse is because we only multiplied the lower number by two, that means we only have 4/8 (only 4 eighth notes are allowed). Multiply the numerator by 2, you get 8/8 (1 and 2 and 3 and 4 and). Even though using eighth notes as a denominator in a simple time signature is kinda rare, it can happen. Stop the metronome. Example of 8/8 in ‘real life’:
This song mixes 7/8, 8/8 and many others. Always keeping the eighth note pulse throughout the whole song, if I’m not mistaken.
Start the metronome again.
The number 3 comes in when you want a different feel to the pulse (that’s why we call it “compound”). That means, instead of a two-part rhythms like before (4 turning into 8). You want a valselike feel to the pulse. Valses have a three-part rhythm. It gives a ‘dragging’ type of feel (4 turns into 12). You know when you see a triplet in 4/4? That’s the default eighth notes for 12/8!! (Ex 2b) The reason we notate them with a number 3 on top (in simple signatures) is to give the musician the understanding that you have a compound feel for just a brief moment.