You are right that giving a 60% discount means 打四折, but this isn't what was asked. The shop will offer a discount up to 60%, as shown in the picture. The word 'discount' can be broken into two, 'dis-' and 'count', with 'dis-' corresponding to 'off'. (And @yuechu has offered an excellent explanation: 'up to 60% off' means '最多享四折優惠'.)
Note that Mandarin and English agree when the discount is in monetary terms (e.g., '享 1,000 元優惠' means 'to enjoy a discount of $1,000'); and that when the discount is in percentage, things somehow get different and admittedly a teeny bit annoying: '享 25% 折扣' actually means '享 75 折優惠'. It is what it is, and maybe there's no good reason.
Oh, and a final note for those who are learning Mandarin: The number in '享 85 折優惠' is always pronounced '八五'.