Yes, but not exactly. The entire $9978 (6765 + 3213) does not carry forward to 2023. Instead, you must use $3000 on your 2022 return. The remaining $6978 carries forward to 2023.
That assumes 2 things: 1. your 2022 income wasn't so low that you couldn't use any of the $3000 capital loss* and 2. the $3213 was your NET loss, for 2022, after adjusting for any capital gains (or you had no gains in 2022).
*A similar question, we see frequently, in this forum is: Do I have to use a capital loss carry over on this year's return. The simple answer is yes. But if your income is low enough, maybe not.
You are allowed to use your standard or itemized deductions to reduce your taxable income before having to use your capital loss.
Technically, if your standard (or itemized) deduction is greater than your AGI, without the capital loss, then all your capital loss is carried forward.