If someone accepts friend request on Facebook account then recent activity link appears on profile, letting all your other friends know you're now friends with the specific person. If you'd prefer to accept a friend request more discretely, and hide the activity from others, immediately remove it from your profile after accepting the friend request.
Facebook Timeline
Sign into your Facebook account. Click on the Friend Request icon next to the "Facebook" logo on the left side of the site header. This brings up your friend requests. Click "Confirm" next to the request.
Click your name on the header's right side to access your profile timeline.
Scroll down beneath the "Friends" column on the right side of the Facebook Timeline. You'll see the "Recent Activity" block.
Click on the "X" next to the "Now Friends With" announcement. Click on "Hide this Recent Activity Story."
Facebook Classic Profile
Sign into your Facebook account. Click on the Friend Request icon next to the "Facebook" logo on the left side of the site header. This brings up your friend requests. Click "Confirm" next to the request.
Click your name in the upper-right corner of the page to access your Facebook profile.
Scroll down your wall until you reach a section labeled "Recent Activity." Here you'll see the "Now Friends With" post.
Hover your mouse over the right side of the post and click on the "X." Click on "Hide this Action from Profile."
Facebook Timeline
Sign into your Facebook account. Click on the Friend Request icon next to the "Facebook" logo on the left side of the site header. This brings up your friend requests. Click "Confirm" next to the request.
Click your name on the header's right side to access your profile timeline.
Scroll down beneath the "Friends" column on the right side of the Facebook Timeline. You'll see the "Recent Activity" block.
Click on the "X" next to the "Now Friends With" announcement. Click on "Hide this Recent Activity Story."
Facebook Classic Profile
Sign into your Facebook account. Click on the Friend Request icon next to the "Facebook" logo on the left side of the site header. This brings up your friend requests. Click "Confirm" next to the request.
Click your name in the upper-right corner of the page to access your Facebook profile.
Scroll down your wall until you reach a section labeled "Recent Activity." Here you'll see the "Now Friends With" post.
Hover your mouse over the right side of the post and click on the "X." Click on "Hide this Action from Profile."