challenge for 英文高手

I think the structure of your sentence is quite good as it is. Apart from the typing error (satistic should be statistics) and the missing spacing from the comma, I would suggest 3 minor changes:
(1) change "conducted" to "released" or "published" because statistics is not an event, like "survey" or "census", so it can not be "conducted".
(2) change "increase by" to "increase of", because we usually would say "the popularity has increased by 6%", or "an increase of 6% in popularity".
(3) it seems "last year at the same time" is perhaps not as smooth as "the same time last year."

My suggestion:
According to the latest statistics published by the government, the popularity of the show is 59%, an increase of 6% comparing with the same time last year, showing that the show is gaining in popularity."

*"an increase of 6% over the same time last year" can also be used.

According to the latest government statistics, the popularity of the show is 59%. With an increase of 6% from the statistics one year ago, this indicates that the show is gaining popularity.