Basically, if the boolean is true, then y is assigned to x. Otherwise, z is assigned to x.
The && is a short-circuiting "and" used between two booleans. If the first boolean evaluates to false, then it's impossible for the expression as a whole to be true, so it "short circuits" and the second is not evaluated. In this example, the short-circuiting is used to test whether paint.getSeq() returns a null value. If it's not null, then it can be dereferenced to call the equals method. But if it is null, then the short circuiting prevents a NullPointerException.
It appears that getSeq() is intended to return a String reference, because the equals method is checking it against a String literal (an empty String, in this case).
So if getSeq is not null, and not an empty String...
"We're kind of on the level of crossword puzzle writers... And no one ever goes to them and gives them an award." ~Joe Strummer sscce.org
Basically, it is calling the getSeq() method of the paint object, which most likely returns a string. The reason I am guessing this is because it then calls the equals() method to compare it to another string.
Next, it is taking a NOT of the equals condition, with the "!" operator. Meaning it is checking to see if it is NOT equals to an empty string.
The next two terms are part of the ternary operator. If the condition is true the value is the first term, otherwise it is the second. So the value is either the string that is returned by calling paint.getPSeq(), or the string "A".