${\color{Green} {ABC}}{\color{Red} {DEF}}=3!3!=36$
Starting with AB or AC or BC and permuted last two elements
${\color{Green} {ABDC}}{\color{Red} {EF}} \text{and}{\color{Green} {ABDC}}{\color{Red} {FE}} =2$
${\color{Green} {ACEB}}{\color{Red} {DF}} \text{and}{\color{Green} {ACEB}}{\color{Red} {FD}} =2$
${\color{Green} {BCFA}}{\color{Red} {DE}} \text{and}{\color{Green} {BCFA}}{\color{Red} {ED}} =2$
Next 6 same as previous and just permuted first 2
${\color{Blue}{BA}\color{Green} {DC}}{\color{Red} {EF}} \text{and}{\color{Blue}{BA}\color{Green} {DC}}{\color{Red} {FE}} =2$
${\color{Blue}{CA}\color{Green} {EB}}{\color{Red} {DF}} \text{and}{\color{Blue}{CA}\color{Green} {EB}}{\color{Red} {FD}} =2$
${\color{Blue}{CB}\color{Green} {FA}}{\color{Red} {DE}} \text{and}{\color{Blue}{CB}\color{Green} {FA}}{\color{Red} {ED}} =2$
Total $48$