Transmission for push-button Barracuda

Somebody has to tell you, so it may as well be me. :( That is what's known as a 318 Poly motor and it will not fit in your 64 Barracuda, because it is too wide. The 318 Poly motors only came in B & C body cars, and also pickup trucks. They never came in Early A body cars like your 64 Barracuda. Sorry to be the bearer of bad news. You need a 318 that came in later years like the early 70's to mid 80's.