ABX3 patterns are very common: most ethyl groups in chiral molecule will have the CH2 protons diastereotopic, and thus form an ABX3 system. As for ABX systems, there is an exact solution, in which one first solves the four AB quartets, which are present in a 1:3:3:1 ratio (i.e., they represent the subspectra resulting from the four combinations of X spins: aaa; aab/aba/baa; abb/bab/bba; bbb). The solutions to these AB quartets give a 1:3:3:1 quartet for the A proton, and another for the B. These can then be solved as first order patterns.
It is not usually necessary to do an exact solution, however, since in almost all cases JAX = JBX (or very nearly so). This means that a first order "AMX" type of solution is quite accurate. What is done here is to treat the pattern as an AB quartet of 1:3:3:1 quartets. In other words, we view the pattern as an AB quartet, each line of which is split by the X3 protons into a 1:3:3:1 quartet. The 1:3:3:1 quartets will have the normal intensity ratios of an AB quartet. To solve, identify the AB-quartet of q and then remove the X coupling. What remains is an AB quartet which can be solved in the usual way. Note that this corresponds exactly to the "AMX" solution for ABX patterns, in which we treat the pattern as an AB quartet, each half of which is split into a doublet by the X nucleus.
The spectra below mimic ABX3 patterns (AB part) of OCH2CH3 groups in chiral molecules. Note that these patterns will get very much more complicated if there is a small chemical shift between the CH2 and CH3 protons i.e., an ABC3 pattern.