An $8,000 balance at 24% costs about $160 a month in interest before a dollar of principal moves. A 0% card with a 3% transfer fee charges $240 once. That's a month and a half of interest to buy eighteen months of none, and on the face of it the math is right.
The number that decides whether it works is the payment. Take the balance plus the fee, $8,240, and divide by the months in the promo. Eighteen months means about $460 a month. If that fits your budget, the transfer clears the debt in eighteen months for $240. The same $460 a month on the old card at 24% takes twenty-two months and costs about $1,930 in interest. So the transfer saves roughly $1,700 and four months. If the $460 doesn't fit, you'll reach the end of the promo with a balance still on it, and that balance goes to the card's regular rate, which is usually as high as the one you left.
The first thing that breaks it is the old card. It's empty now, and empty cards get used. Twelve months later there's a balance on both, which is the outcome the transfer was supposed to prevent. Cut it up, or at least take it out of your phone's wallet. The second is a late payment. Most promo terms end the 0% the moment you're late, so put the payment on autopay for the amount you calculated, not the minimum. The third is new purchases on the new card. They usually don't get the promo rate, and while you carry the transferred balance you may not get a grace period on them either, so the card is for the old debt and nothing else.
Your credit score takes a small hit from the application and a bigger one if the new card ends up near its limit, since utilization is a large part of the score. It recovers as the balance drops. That's a fair price for eighteen months of zero interest. It's not a fair price for eighteen months of minimum payments.
Whether you transfer or not, the payoff order for everything else follows the same logic as snowball or avalanche. The transfer makes one of the balances temporarily free, and free balances get paid last in an avalanche, so make sure you don't let the promo run out while you're attacking something else.
Run the division before you apply: balance plus fee, divided by promo months. If that payment fits, make the transfer and set the autopay the same day. If it doesn't, the transfer only delays the problem, and the better move is the payment you can sustain on the card you already have.