There are couple of different options. The first would have you turn the equity into cash through either a refinance or a home equity loan. You can then use these funds for the down payment on the new property.
The other option is called a cross-collateral loan. This is going to be more difficult to qualify for as most lenders will need to have their lien in the first position on both properties.
Taking the cash out with a home equity loan is going to be the best option. It is easier and in most cases less expensive. The only thing you will need to consider is the ability to qualify for a mortgage while carrying both properties.