Motion by a fourth means the next root sits four letter-steps up, or five down. The ear often hears that as a strong step toward home.
You can feel it without naming every interval. Play two chords. If the second one answers the first, you have met the motion.
This guide points at one long pattern and one short cadence. Both live in the pattern list. Neither is a song.
ii–V–I Cadence is ii, V, then I. In C that is Dm, G, then C. Dm up to G is a fourth. G up to C is a fourth.
Play it slowly on the Chord progression player. Hold each chord for a bar. Hum the root as you change so you hear the step, not only the colour.
The pattern is written as triads. A jazz book might use sevenths. Here the grip stays a triad so the step is easy to hear.
C major is the home used in that example. Move the key chip if you want the same step in G or F. The Roman numbers stay. The letters change.
Circle of Fifths walks through most of the key, one strong step at a time. The page lists the degrees. Read them there. Do not memorize a string from this paragraph.
A step down a fifth is the same loop as a step up a fourth, facing the other way. If that sentence is too much, ignore it and just play the pattern.
The circle is a practice loop. It is not the chart of a hit. Play two rounds. Stop. Your ear will remember more than a third rushed round.
G major and F major are other places to run the same loop. Pick one key per day.
Ode to Joy moves among C, G, Am and F. G to C is the fourth into home. You can feel that arrival even inside a four-chord tune.
Amazing Grace moves G, C and D. C to G, in the key of G, is a fourth back toward home. The hymn is not a circle. It still uses the step.
Auld Lang Syne and Simple Gifts give you more chances to hear a chord answer the one before it. Name the roots out loud once. Then stop naming and play.
If the motion is unclear, slow down until each chord is a place you could stay. Speed hides the step. Stillness shows it.