Click "Use a formula to determine which cells to format"
Type =COUNTIFS($B$3:$B$15,$B3,$C$3:$C$15,$C3,$D$3:$D$15,$D3)>1 in "Format values where this formula is TRUE" window.
Click "Format.." button
Click "Fill" tab
Select a color for highlighting cells.
How the conditional formatting formula works
Step 1 - Count rows which match the current row
The COUNTIFS function allows you to counts duplicate records, make sure you create a condition for each column in your record. There are three columns in this example, the first argument is $B$3:$B$15 and doesn't change when the conditional formatting moves on to the next row.
The second argument is $B3 and is locked to column B, however, the row is a relative cell reference (not locked) and changes when the CF moves to next row.
If there are rows that match all three conditions $B3, $C3 and $D3 the COUNTIFS function return the number of rows that match.