"This is my way of solving things."
Translation:Este é meu jeito de resolver as coisas.
Not in this case. In Portuguese we have 3 genders for this kind of pronoun. Indeed, Este is the masculine form, esta the feminine and isto is a kind of neuter. It would be equivalent to 'it' in English. In this case, one should agree gender to pronoun, eg: este é meu modo de resolver problemas, or esta é minha maneira de resolver problemas. Both are right, although Duolingo may not accept the later. Understand, isto is not wrong, but it would sounds odd, weird. It is better to agree, in this case, to the noun.
If I understood right your question, it´s incorrect mate. In english, the gerund may be used as a kind of infinitive. In portuguese, you will use the infinitive, in this case, thus, this is my way of resolving things has to be translated as 'esta é minha maneira de RESOLVER as coisas'. There is a rule mate, you use the gerund: 'ando, endo, indo', when you have a progressive action, as , for example, in 'I am eating'. Works for past too.'eu estava comendo= i was eating'. and so on. The infinite, or 'ar, er, ir' is used when the verb follows a preposition, as in the case 'minha maneira DE resolver' Hope to help.