matching numbers in two different data frames

I have two data frames: x contains two columns: A & B:

A      B4      16      29      210     315     3

data frame y contains several columns, of which two of them are of interest in my analysis:

C       D6      54915     6314      34410     209

Note that column C in data frame y contains some (but not all) of the values available in column A of data frame x.

What I would like to do is to find the rows that there is match between x$A and y$D, then add the corresponding value in column D to my data frame x. So the resulting x would look like:

A      B    D 4      1    344 6      2    549 9      2    NA 10     3    209 15     3    631