Solution 1:

You can count the number of occurrences of "A", "B" and "C" in each row using COUNTIF, and then add the results together. If any of those values are present in a row, the sum should return a non-zero value.

Try this:

Go to Conditional Formating > New Rule > Use a formula to determine which cells to format

Enter this formula:

=(COUNTIF($D2:$L2, "A")+COUNTIF($D2:$L2, "B")+COUNTIF($D2:$L2, "C"))>0

Set your format and click OK.
Make sure that the Applies to box in the Conditional Formatting Manager window is set to =$D2:$L2, or the row(s)/range(s) that you wish to apply the conditions to.

These should also work:

=COUNTIF($D2:$L2, "A")+COUNTIF($D2:$L2, "B")+COUNTIF($D2:$L2, "C")

=COUNTIF(2:2, "A")+COUNTIF(2:2, "B")+COUNTIF(2:2, "C")

Solution 2:

Enter this as your conditional format formula:

=SUMPRODUCT(1 * OR(IFERROR(FIND("A", $D$2:$L$2), FALSE),
                   IFERROR(FIND("B", $D$2:$L$2), FALSE),
                   IFERROR(FIND("C", $D$2:$L$2), FALSE)))

SUMPRODUCT treats the range as an array formula would, checking the FIND on each cell, if it ends up finding even one instance of the letters then it will end up true.