Junk, or combination, defenses feature one or two defenders playing tight man-to-man denial defense on your best player(s), while the remaining defenders play a zone. These defenses are usually used against teams with one or two star perimeter players. Examples are the "box-and-1", the "triangle-and-2", the "diamond-and-1", the "1-3 and a chaser", and others.
In attacking these defenses, if you want to keep things very simple... some coaches simply advise using your favorite zone offense vs box-and-1 defenses, and your regular man-to-man offense vs the triangle-and-2 defense. Here, we'll discuss the "BB-offense" ("Big-Blocker") that can be used against most of these defenses. Also see "Attacking the Box and 1 Defense" (more specific X's-and-O's)
With the box-and-1, the defense puts a defender (X2) tight on our best player O2, while the four remaining defenders set up in a "box" zone with X4 and X5 on the low blocks and X1 and X3 at the elbows.
Here, we have our "BB" O5 set up along the lane, same side as O2. O1 engages the top defender on O2's side, as O2 slides down half-way to the corner. O5 back-screens X2, and O2 cuts around the screen (either above or below the screen, depending on where the X2 defender is), cuts into the middle of the box for a pass and pull-up jump-shot.
O4 again ducks inside underneath for a possible pass. If the X4 defender comes up to defend O2, O5 seals X2 and back-cuts to the hoop for the pass from O2 (or a high lob directly from O1).