Your partner has done a Takeout double after SOUTH's 1D. They have a maximum of 2 hearts and a minimum of 3 of the other suits and ask you to call your best suit. NORTH has responded with 1H so you do not have to bid. However you have 9 HCPs (you should only bid if you have >8 HCPs) but you do not have a stopper in hearts so cannot bid 1NT. You should bid 2C.
Your partner has been forced to bid their best suit but may not have many points. As you do not have 16 points you should PASS.
You need to tell your partner that you cannot support hearts and that you have 6 clubs. If you bid 2C that can be a limiting bid so to tell your partner that you have points bid 3C.