The backtrack vocabulary implements simple non-determinism by selecting an element of a sequence, performing a test and backtracking to select the next element if the test fails.

Find a first successful element:

Find all combinations of successful elements:

Select elements from a sequence:

Examples
Let's solve the following puzzle: a farmer has some chickens and some cows for a total of 30 animal, and the animals have 74 legs in total.
: check ( chickens cows -- ? ) [ + 30 = ] [ 4 * swap 2 * + 74 = ] 2bi and ; [ 1 30 [a..b] amb 1 30 [a..b] amb [ check must-be-true ] [ 2array ] 2bi ] bag-of .
V{ { 23 7 } }

The output means there is only one solution: the farmer has 23 chickens and 7 cows. If we want to only find the first solution, the following approach could be used:
: check ( chickens cows -- ? ) [ + 30 = ] [ 4 * swap 2 * + 74 = ] 2bi and ; [ 1 30 [a..b] amb 1 30 [a..b] amb 2dup check must-be-true "%d chickens, %d cows\n" printf t ] [ "No solution." print ] if-amb drop
23 chickens, 7 cows

See more examples here: https://re.factorcode.org/tags/backtrack.html