Though 'scholar' has already been thoroughly trounced, it's also worth noting that VAT 4956 identifies the summer solstice on the 9th day of the 3rd month.
The solstice is usually 20 or 21 June in recent years on our modern calendar; it can
be as late as 23 June but no later. For Julian dates in the distant past, the period shifts because the Julian calendar
differs by about a day for every 400 years compared to the Gregorian
calendar. Hence, for the Neo-Babylonian period in question, the Julian date of the summer solstice must fall within the range of 26-29 June (or 30 June if we round up the difference between 588BCE and now to 2800).
For 568BCE, the 9th day of the 3rd month corresponds to 29 June (Julian calendar), which is a perfect fit for the solstice in that period.
But for the Watch Tower Society's nonsensical assertion about Nisan beginning on 3 May in 588BCE, this would put the summer solstice on 9 July, which, again, is impossible.