Most contemporary singing lives in the middle of the voice, where chest and head overlap. That overlap is the mix, and the spot where the voice wants to switch from one to the other is the passaggio, or bridge, or break. Cracks happen there. So do strained high notes and thin, disconnected ones. If you have done lessons six and seven, you now know what each side of the bridge feels like, and this lesson is about crossing it.
Two things to know first. Cracking is normal, including for trained singers, and an occasional crack is not harmful in itself; forcing through it with volume is what to avoid. The guide on why voices crack covers that in detail if the cracking has been discouraging you. And there is no single agreed method for building mix. The two exercises here approach the bridge from opposite directions, and that is deliberate.
What to notice
"Bub" is a descending arpeggio, 8-5-3-1, that starts on the high note and comes down. Entering at the top puts you in head-mix, and the soft "b" keeps the airflow easy, so the descent carries some of that lightness down into chest. The keys start low, climb through the passaggio, and come back down again, so you cross the bridge in both directions.
"Goog" is an octave arpeggio up and back, from the Speech Level Singing tradition. The hard "g" and the narrow "oo" vowel are meant, in that method, to keep the larynx from rising while the line takes you through the bridge. Keep the vowel small here. Belt-oriented teaching opens vowels through the same notes, but that is a different exercise with a different aim.
In both, the notes to watch on the breakdown are the ones just above where your voice wants to flip. If those notes score wildly off while the rest are fine, that is the bridge showing itself. A common reading: slightly flat and heavy suggests carrying chest too high; thin and unstable suggests letting go too early. Treat it as a hypothesis to test, not a diagnosis.
What done means
Sing both, log them, and find your bridge on the breakdown. You are done when you know which notes it lives on. Smoothing it is weeks of work, not one session, and that is what the routine is for.
Add whichever of the two felt more possible. Most singers find "bub" easier at first because it comes down instead of up.
The exercises
Bub Mix Voice
About this exercise
A descending major arpeggio (8-5-3-1) sung on a relaxed 'bub' to coordinate a connected mix from the top down. Entering on the octave above the tonic places the voice in head-mix, and the lip-and-vowel 'bub' onset keeps the airflow buoyant so the descent through the arpeggio carries head resonance down into chest without weight or pushing. Keys begin at the bottom of the range, climb a half step per iteration up through the passaggio, then descend back down, working the mix in both directions.
A Speech Level Singing staple that coordinates mix registration through the first passaggio. The hard 'G' onset with a narrow 'oo' vowel is meant, in that method, to keep the larynx from rising while the octave arc takes the voice through the bridge and back, training the sensation of a consistent tonal 'core' across registers.