Complex sentence: He played with the Jerry Wald band before joining Woody Herman in 1944 as a member of the First Herd and in 1946 he played with Benny Goodman and Jack Teagarden.
Split into simpler sentences: He played with the Jerry Wald band before joining Woody Herman in 1944 as a member of the 1st Herd. And in 1946 he played with Benny Goodman and Jack Teagarden.