"i had a miscarriage on the 24th of june, is it possible for me to get get pregnant if i had sex on the 10th - 14th of july"

Yes.

Any time you have sex, pregnancy is possible, even after a miscarriage.

You'll have to wait until your period is at least 2 weeks late, then test using first morning urine. If that test is negative, wait for your next period and if you miss it, test again or get a blood test.

Keep in mind that your period may be off for a while due to the miscarriage, and you could also get a false positive because the pregnancy hormones are still in your body.