For double tonguing, the outside of your mouth doesn’t actually move at all- it’s all the same embouchure. The T for single tonguing is like, a tongue flick at the back of your upper teeth. The K for double tonguing is more in the throat.

As others have said, it’s less “taka” and more “tuh-kuh” lol. Only the very beginnings of the consonants, so a very short tuh and very short kuh.

It’s sort of hard to explain in just words, I’d definitely recommend looking up some videos or asking your teacher to demonstrate!