Property tax is not shown in full amount on my Rental Properties and Royalties (Sch E) [Expenses] and not shown in full on Deductions & Credits section [Property (Real Estate) Taxes]

Hello, Tax experts. I need help with my Property tax under Rental Properties and Royalties (Sch E)  and the Deductions & Credits section.

 

(Edited) I rented my whole house out started 1July last year (personal use 1Jan-20Jun). I entered my rental income under Wages&Income --> Rental Properties and Royalties (Sch E).  I also entered 'Real estate taxes' $8,740 from 1098 as expenses.  but 1. my property tax under expenses is only shown as $4,517 (See attachment 1), why is that?   2. When I moved to the Deductions & Credits section. My Property (Real Estate) Taxe is only shown as $4,223 instead of $8,740.  it also said 

We already deducted the personal portion of your property taxes from your rental property in the amount of $4223.00, so don't enter that amount here"            (See attachment 2).
 
My question is why is only $4,517 or $4,223  instead of  $8,740 on my 1098? Should I enter the difference to match with $8,740 or should I just leave it because now it's a rental property, not a primary home anymore?
 
Thank you in advance!
 
 
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