The first thing you should do with date variables is confirm that R reads it as a Date. To do this, for the variable (i.e. vector/column) called Date, in the data frame called EPL2011_12, input
class(EPL2011_12$Date)
The output should read [1] "Date". If it doesn't, you should format it as a date by inputting
EPL2011_12$Date <- as.Date(EPL2011_12$Date, "%d-%m-%y")
Note that the hyphens in the date format ("%d-%m-%y") above can also be slashes ("%d/%m/%y"). Confirm that R sees it as a Date. If it doesn't, try a different formatting command
EPL2011_12$Date <- format(EPL2011_12$Date, format="%d/%m/%y")
Once you have it in Date format, you can use the subset command, or you can use brackets
WhateverYouWant <- EPL2011_12[EPL2011_12$Date > as.Date("2014-12-15"),]