On the Great Plains, 19 century settlers used mud and grass to build their homes, making do without timher and nails.
How can you explain making do???
"To make to with[out]" is an English expression equivalent to "To get by with[out]."
The preposition "with" is essential.
If I may supplement the Great JPs answer, I would like to add that the implication for both expressions is that you're are "making do" or "getting by" with less resources that what is normally required to complete the task, typically "making do" without what would normally be considered an "essential" one.
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993