The correct option is E Programs that enable a family with insufficient savings for a conventional down payment to move into new housing and to apply
In option A, the use of 'enable' and then 'to be able' in the same line is illogical and redundant as both mean the same thing (we wouldn't normally hear this because there's a phrase in-between). Its the same with E. Since, the sentence is one of parallel structure, the correct answer should confirm to parallelism- 'to move' should be parallel to 'and to apply'. This doesn't happen with D- 'to move' is not parallel 'to applying'. In C, 'that' follows a semi-colon which, grammatically, refers back to all that happened before the semi-colon. This is not appropriate in this context as 'that' should refer to 'programs'. Thus, B is the only correct option.