Assuming you have made no prior Roth IRA distributions, you have not previously used any of your lifetime $10,000 exemption for a first-home purchase and you qualify as a first-home purchaser (neither you nor your spouse had an interest in a first home in the 2-year period preceding the purchase of the first home), you can withdraw $49,000 from your own Roth IRAs tax and penalty free for the purchase of your first home. The first $39,000 that comes out will be your original contributions, tax and penalty free no matter what you use the money for. The remainder will be a distribution of earnings. Since you've had a Roth IRA for more than 5 years, the first $10,000 of earnings distributed will be a first-home qualified distribution, tax and penalty free, but will still be required to be reported on Form 8606 Part III (to determine it's nontaxable) and on Form 5329 (to eliminate the penalty). You can also withdraw any amount up to the entire balance in your Roth IRAs, but the portion beyond $49,000 will be subject to both tax and penalty unless you are over age 59½ or disabled.
As I understand it, you've already received distributions of $38,000, bringing your total assets in the Roth IRA down to $11067.27, That would suggest that the earnings in the account are actually $10,067.27, not $10,330.22, assuming that you have made no prior Roth IRA distributions. Perhaps the $10,330.22 is showing investment performance only, not Roth IRA earnings net of any account for fees deducted by the custodian, or is a value that is not updated daily. Also, a Roth IRA custodian can only report investment performance of a particular account. If you have more than one Roth IRA account your Roth IRA earnings is the aggregate balance in your Roth IRAs minus your remaining contribution (and Roth conversion) basis.
Also, the Roth IRA custodian has no need to know what you are using the money for unless the purchase is delayed or cancelled and you need to roll the $10,000 that qualifies for the first-home purchase exception back into the Roth IRA after the normal 60-day rollover deadline but before the 120-day deadline for doing so, in which case the Roth IRA custodian only needs to know at the time of the rollover that this is a rollover of a first-home purchase distribution.
Depending on the performance in the Roth IRA between the time of your $6,000 contribution for 2019 and now, it might be better to obtain a return of contribution of $6,000 rather than a regular distribution of that portion. If there have been overall losses in the account since the date of the distribution (after adding back the $38,000 already distributed), a return of $6,000 would result in a distribution of an amount adjusted for the overall losses, something less than $6,000. If there have been investment gains, the distribution would be an amount adjusted upward, with the amount distributed over $6,000 being subject to tax and penalty. Obtaining this return of contribution would preserve the opportunity to make a new $6,000 contribution for 2019 later (until April 15, 2020) to put some money back into a Roth IRA regardless of whether or not you complete the first-home purchase. (If you obtain a return of contribution of $6,000, your original contribution basis drops to $33,000, making $5,000 of your $38,000 already distributed be a distribution of earnings to which you would need to apply the first-home purchase exception, leaving only $5,000 of the exception available for additional distributions.)
